If you are in Luxembourg, chances are that you are staying in Luxembourg City, so getting in will not be a problem. If you are staying elsewhere then just remember that all buses and trains lead to Luxembourg City. See Luxembourg#Get in for details on getting into the country.
The best way to get around Luxembourg is by foot, bike and bus. Due to the city's small size and beautiful scenery, by foot is also the best way to appreciate it. In a few hours (or dividing your trip in two days) you can get to know the whole city on foot. Buses are regular and they all pass through the central bus station Hamilius.
The city also operates a self-service bike scheme and the stations can be found in various locations around the city centre. For more information check the Ville de Luxembourg (VDL) website. 
Also in the city is the country's main railway station and this can be got to by most buses. The station is a good way of getting around the country or speedily getting into any of the neighbouring countries.
The Casemates Bock is a network of underground fortifications, built in the 18th century. The fortifications and environs are recognized as a UNESCO World Heritage Site.
The Bock itself is the rock on which the first castle stood, founded in 963 by Sigefroy (Sigfried). It is tied to a number of other remains of the old fortifications. Among others, the famous fortress builder Vauban built much in the city.
The river of Luxembourg is the Alzette, which is very small now, but because the sandstone of the area is very soft, it dug out a huge valley. This is called the Ville Basse and is a spectacular area particularly the Grund (Statgrond) which is well worth the time to take a stroll around. The old fortress surrounded this valley. The Venceslas walk (named after Venceslas, Czech king and count of Luxembourg who built much of the fortresses around) leads along the fortresses, protecting the city on one side (and now forming one of the most spectacular "balconies", the Corniche) and the fortress of the Raam plateau on the other. In the Grund itself you can find a lot of pubs and the....
Neumünster Abbey, now a cultural and encounter center with a nice church and the old St. John's hospital.
The pedestrianized old town is where the greatest concentration of (rather expensive) shops as well as bars and restaurants are to be found. Specific sights are few but all around town you can spot details that remind you of Luxembourg's historical value.
Just near the Hamilius bus station are Place Guillaume and the Place d'Armes. Place Guillaume (also known in Luxembourgish as the Knuedler) is the venue for a market every Wednesday and Saturday. It is also the site of an equestrian statue of William II of the Netherlands and Luxembourg and the neo-classical Town Hall which is fronted by two bronze lions summer months the Place d'Armes is filled with tables and chairs from the surroundng cafes and at the centre of the square is the bandstand around which various concert seasons are based.
Just off the Place Guillaume is the Grand Ducal Palace which was fully restored during the nineties. It also houses the Luxembourgish Parliament the Chamber of Deputies.
Also of note is the Cathedrale de Notre Dame. This was built between 1613 and 1618 by Jesuits and was elevated to the status of cathedral in 1870. Nearby is the Gëlle Fra: literally 'Golden Lady'. This is a golden figure of a woman holding a wreath a symbol of victory. It was taken down by the Nazi's during occupation but stands today as a memorial to those who gave their lives in World War II.
Nearby Gëlle Fra and Place de la Constitution is the entrance to the Pétrusse Casemates which were constructed by the Spanish in 17th century. They are not as large as the Bock Casements.
On the road from the inner city to the Bock you will find the Eglise St. Michel. This church took on its present form in 1688, but was probably built in the early 14th century. It was restored during 2003 and 2004.
Luxembourg American Cemetery and Memorial
World War II Luxembourg American Cemetery and Memorial, in the eastern section of Luxembourg City, just south of the airport, . Open daily except for December 25 and January 1; 9AM-5PM. The Cemetery is the final resting place for 5,076 American military Dead, most lost during the Battle of the Bulge. It is also the final resting place for General George Patton. A monument is inscribed with the names of 371 Americans whose remains were never found or identified. Two large stone pylons with operations maps made of inlaid granite describe the achievements of American armed forces in the region during World War II. Free.
The Kirchberg area houses a number of banks and most of the European institutions in Luxembourg (Parlament, Court of Justice, Court of Auditors, European Investment Bank and some of the Commission's Directorate Generals. A number of buildings were build by celebrated architects like Richard Meyer and Gottfried Benn. Some modern sculptures also appear between the buildings.
MUDAM (Musée d'Art Moderne Grand-Duc Jean), 3, Park Dräi Eechelen (Kirchberg, buses 1,3,6,Eurobus), . Designed by I.M. Pei of "Louvre Pyramid" fame, this museum showcases Luxembourgish artists and changing international exhibitions. The nonlinear (and rather confusing) building is half the fun, and on a quiet weekday afternoon in the off season you'll pretty much have the place to yourself.€5. edit
Cemetery for German soldiers at Sandweiler, Deutscher Soldatenfriedhof; L-5280 Sandweiler, ☎ (+352) 35 50 07, . Is a World War II cemetery in Sandweiler, in southern Luxembourg. It contains the graves of 10,913 German servicemen from the Battle of the Bulge in winter 1944 and spring 1945. It is 1.5 km from the Luxembourg American Cemetery and Memorial. Devoted to the fallen German soldiers from one of the bloodiest battles of World War II. A touching memorial. edit
Schueberfouer, Glacis. Held every year across 2 weeks during end of August and early September, this huge and historic funfair attracts enormous crowds. As well as the many stomach churning rides there are numerous places to eat and drink to your heart's content. An important date in the social calender of young Luxembourgers.edit
Grand Duke's Birthday. Not the actual birthday of the current Grand Duke (or any preceeding for that matter) the 23rd June is the country's national day. All night street parties, fireworks and parades are enjoyed by seemingly the entire population of the country on the evening preceding the holiday. edit
Grand Ducal Palace, Rue du Marché aux Herbes, Luxembourg. The Palace is open for a period of 6 weeks over July and August whilst the Grand Duke and his family are away on their holidays. Guided tours last for about 1 h, are inexpensive, and are available in various languages, including English. Tickets are available from the tourist office in Place de Guillaume II. edit
Sofitel Hotel Bar and Restaurant, 40 boulevard d´Avranches , L-1160, Luxembourg (train station). One of the very finest panoramic views available of the city is to be found from the top floor bar of this building. If you arein the area, it is worth stopping in for a quick drink.edit
Home to a suprisingly high number of Michelin star establishments, the city houses many fine eateries. Luxembourg also has a very large population of Italians that came to the country in the late 19th century so Pizzerias in Luxembourg are always very reliable and frequent. For something cheap and quick the Place d'Armes is the best bet.
La Fontaine, 25, place de Paris, ☎ +352-494076. One of a number of affordable bistros clustered around place de Paris, conveniently located halfway between the station and the old city. The quadrilingual menus run the gamut from pizza and mussels to Luxembourgish classics like judd mat gaardebounen (smoked pork neck with broad beans), and there are daily specials for around €8.€15-20. edit
Taj Mahal, 2, rue de Strasbourg, ☎ (352) 40 59 41. By anyone's standards, a fantastic curry house serving rich and delicious Indian food. Very friendly staff too. Well worth making the short trip from the centre to this restaurant located near the station.edit
Mousel Cantine, 46, Montée de Clausen. Great local plates on the site of the former Mousel brewery. Wash down huge portions of pork knee and broad beans with tankards of Mousel lager.edit
Le Palais D'Asie, 47, avenue de la Liberté. Don kimonos and marvel at the skill of the chefs as they prepare Japanese and Chinese style cuisine before your very eyes including ceiling-high flames and an "egg show". As entertaining as it is tasty. Arrive hungry as the portions are generous.edit
Luxembourg is a decent place to have a drink. Due to the amount of ex-pats who live in Luxembourg there are a wide variety of establishments in addition to the Luxembourgish bars. Pubs in Luxembourg tend to be a traditional affair, although more modern bars, and English or Irish themed pubs have also become the norm. English themed pubs
Britannia Pub. The favourite watering hole of local English ex-pats. Good place for watching football.
Ecosse. Scottish themed bar. Can be extremely crowded and lively during international rugby and football matches but generally a quiet place for a pint.
Pygmalion. Irish pub and the best of the English, Scottish, Irish triumvirate situated in Clausen. Pub quizzes every other Monday.
Scott's,  No. 4, Bisserwee (down in the Grund). A common place for a drink (or two).
Urban, . A refreshingly modern bar that has a wide mix of clientèle. Although often overcrowded it is a great place to start a night out. Urban also has live music every Sunday evening and has sporting events shown on two massive plasma screens.
The Tube. Subterranean, London underground themed bar. International young crowd and great tunes for various tastes. Gets extremely packed late on Fridays and Saturdays and overspills into the street during warmer months.edit
Vis-a-vis, Rue Beaumont 2 (Near Place d'Armes), ☎ 352 46 03 26. Hang out with the locals in this charming little Luxembourg-ish bar. Cheaper than a lot of other watering holes found in the city. edit
Café des Artistes, (Grund). Smokey little Luxembourg piano bar illuminated by candlelight. edit
Melusina. Has a large main room with a balcony. It also has another couple of rooms at the back of the club which are worth a look.
Muko Muko. Located near the big parking lot (Glacis) just outside of the centre, but worth the walk there. No heels are too high and no skirts/shorts are too short here.
Camping Bon Acceuil, . In Alzingen 4 km to the south of the city. One hundred pitches. Adult €4, kid €2, pitch €5.
Luxembourg Youth Hostel, . 2, rue du Fort Olisy, tel: (352) 22 68 89 20. A nice clean hostel with a friendly atmosphere and only 10 minutes on the bus from the city centre. 23.90€ per bed in a shared dorm, discount with HI membership. Breakfast free, other meals €5 - €10.
Ibis Luxembourg Sud, , rue de Turi. Located just south of the city and visible from the highway is a good alternative. July 2011 prices were 79€, or 59€ if booked in advance.
Hotel Empire, , 34, place de la Gare. Located right across from central station. Small rooms, but cheap and a good location. July 2011 prices were 65€ for single occupancy, 75€ for double. Has indoor storage for bikes as well as an air compressor and tool kit. Breakfast included.
Sofitel Luxembourg Europe is an Accor Hotels group luxury property located in Plateau de Kirchberg, in the North European Quarter. Comfortable beds and a famous Italian restaurant.
Hôtel Albert Premier, 2a, Rue Albert Premier 1er, ☎ 00 352 442 4421 (AlbertILA@ila-chateau.com, fax: 00 352 447 441), . Elegant four star hotel situated close to the old city and Central railway station. 42 rooms with en-suite bathrooms, restaurant, internet access, sauna, fitness room, garage, meeting facilities.€150-480. (49.60908,6.11824)edit
Try to show respect for the local language and make some effort to say a word or two of it even if it's just the standard greeting "Moien". Luxembourg is a low-key capital city and is generally not the best place for big nights out although during the months of warmer weather it can have its moments.
Luxembourg is a safer environment than most other European capital cities, and it would be rare to encounter any physical threat. Nevertheless, care is required in and around the train station area (especially late at night), which contains a handful of seedy clubs and prostitutes.
This is a usable article. It has information for getting in as well as some complete entries for restaurants and hotels. An adventurous person could use this article, but please plunge forward and help it grow!