The best and most convenient way is by train. Deutsche Bahn offers direct connections from Berlin, Leipzig and Erfurt. Weimar Hauptbahnhof is about a kilometre from Goetheplatz, in the city's center: you can
walk: A pleasant ten-minute stroll downhill is a good way to stretch your legs after the train-ride. Cross the square in front of the station and walk down Carl-August-Allee. Go around the right of the building at the end of this road (the Neues Museum), and continue walking in the same direction, now on Karl-Liebknecht-Strasse, continue across the crossing and you soon find yourself in the city centre.
take a bus: lines 2, 3, 3A, 3B, and 6 will bring you to Goetheplatz within a few minutes. One-way tickets cost EUR 1.60.
Weimar is small and the best way is by foot or bike. Weimar has a public transport system but as a tourist you won't need it. Taxis are at night the best way when you feel lost and they are used to cater tourists.
Weimar is one of the most historic sites in Germany. It was home of Goethe and Schiller, the two most famous German poets and writers.
Bauhaus-University Weimar and the Haus am Horn, part of the Bauhaus Sites protected by UNESCO .
Stadtschloss (city castle) - Home of the biggest sponsor of Goethe and Schiller. Art gallery.
Anna Amalia Bibliothek - Unique library and art selection, famous for it's rococo style. A fire in 2004 did great damage but the library reopened in 2007.
Nationaltheater - Foundation place of the first German democracy in 1918 and successor of the Weimar Hof theatre where Goethe's premieres took place. Well-known theatre today.
Park an der Ilm - Picturesque garden with Goethes summer house. Lie down on the lawn and enjoy the scenery.
Belvedere - charming park with summer castle a short distance to the south of the city
Goethe- and Schiller-Memorial in the Theaterplatz - This is a very famous memorial for two great German writers.
Buchenwald - for a more somber outing, one can visit the famous Jewish concentration camp, just over the hill from Weimar in Ettersberg. It's a 20 minute bus ride from the train station. The Stalinist monument erected outside the camp once the Soviets took over is visible from the city.
The best thing is to take a guided tour through the town because most buildings have a story. Either you have time or plan a tour through all buildings of interest.
Inexpensive self-guided GPS audio walking tours are available from the tourist information section in English, French and German.
The nation of poets and thinkers (Land der Dichter und Denker) became a country of judges and hangmen(Richter und Henker) in the period from 1933-45. To complement the experience of Weimar, the cultural capital, make the short trip to the Buchenwald Memorial  just 10 kilometers outside town. This is a good experience to see how close genius and nightmare of German history can come.
An excellent introduction to Weimar is Weimar Haus: Das Geschichtserlebnis (in English, "The History Experience"). This is an interactive multimedia tour (choice of languages) through Weimar's history from prehistoric times to the present. It features audio, video, wax figures and detailed sets you move through guided by famous historical figures. Schillerstr. 16.
The market square is the home of the centuries-old and extremely tasty Thueringer Bratwurst, which can be bought at one of the many sausage stands during the day. It is widely considered a delicacy. The area is also famous for its cakes, such as the Zupfkuchen, all widely available generally costing around one euro.
There are many good restaurants in the city catering to the tourist market selling all manner of cuisine, and with the compact nature of the city you can never be far away from the food you are wanting.
Pizzeria Da Antonio, Windischenstraße 33, Weimar. 10.00-24.00. A friendly, cheap italian restaurant with 90 main dishes to choose from, including 45 types of pizza and many salads or pasta dishes. Average dish price €6-7.50, 0.5l of soft drink or beer around €2.50.Main dishes all between €4.50-9.00. edit
Labyrinth Hostel Weimar Goetheplatz 6, Tel.: 0178-7487579, E-Mail - Right in the center of town, a new youth hostel and Weimar's first private hostel. Prices from 10 €, a bed in a double costs from 20 €
Das Hababusch Hostel, Geleitstr. 4, ☎ 03643 850737 (firstname.lastname@example.org, fax: 03643 402615), . checkin: 9am; checkout: 10am-noon. Very central, affordable but a little grungy. It is altogether quite small, so it's a good idea to book ahead of time if possible.€12.50 (dm) / €17.50 (d) / €22.50 (s). edit
DJH Jugendherberge Am Poseckschen Garten, Humboldtstr. 17, ☎ 03643 850792 (email@example.com, fax: 03643 850793), . Near the historical graveyard, this hostel is a bit out of the way. A ten minute walk will bring you downtown, though, and bus-line #6 stops nearby too (Cranachstrasse).~€20. edit
Comfort Hotel Weimar (Comfort Hotel Weimar), Ernst-Busse-Straße 4 99427 Weimar, ☎ +49-(0)3643 / 455-0, . The hotel is located in the northern part of Weimar, only 10 minutes drive from the city centre, and has its own free car park. Easy access A4 motorway (Autobahn A 4) or the local public transport system.(51.011398891,11.331603527)edit
Best Western Premier Grand Hotel Russischer Hof, Goetheplatz 2, ☎ +49 (0)3643-7740 (firstname.lastname@example.org, fax: +49 (0)3643-774840), . The Hotel is located within the historical part of Weimar and all points of interest are within walking distance. edit