Göttingen is a city in the southernmost part of the German state of Lower Saxony, bordering Hesse and Thuringia. The population of Göttingen in 2004 was 129,446, of which around 30,000 are students. It is best known for being the home of the Georg-August-Universität Göttingen , as well as the site where the prestigious Max Planck Society (a German organization for scientific research) was founded in 1948. The Max Planck Institutes for Dynamics and Self-Organization, for Experimental Medicine, for Biophysical Chemistry, and for History are all located in Göttingen. 44 Nobel Prize winners  have studied or taught in the city, and these and other notable former Göttingen residents are commemorated by white plaques on many buildings throughout the town. Its nickname is therefore the Stadt der Wissenschaft (City of Science). Today, Göttingen is a charming university town, off the radar screen for most English-speaking tourists but well worth a visit.
Göttingen lies in the very center of Germany and is easily accessible from most parts of the country. It has no airport, but can be easily reached by train  or car from larger cities that do. Göttingen's Hauptbahnhof is a stop on the ICE (Inter City Express) train line between Hamburg and Munich and also on the ICE line between Berlin and the South of Germany. Göttingen is approximately half an hour to Hanover, two hours to Hamburg, three hours to Berlin, four hours to Munich, and two hours to Frankfurt.
Göttingen has an extensive bus network which criss-crosses the city center and extends out to the surrounding. Information about the city bus network is available from the Goettingen Verkehrsbetriebe  (under Fahrplanauskunft, click "Netzplan" for a map and "Einzelfahrpläne" for schedules). A single ride within Göttingen costs €2.00; for multiple trips, save money by asking for the €7.00 "Viererkarte" (four tickets at once) or the "Achterkarte" (eight tickets) for €13.00.
There is a nice self-guided City Walk on the city's tourism website, which takes you by all the main sites. Highlights include:
Altes Rathaus (town hall), Marktplatz. Built 1369-1444, the Altes Rathaus was the town hall until 1978, and it now houses the Tourist Office. The coats of arms of other members of the Hanseatic League are painted on the walls.
Gänseliesel (goose girl), Marktplatz. This fountain outside the Altes Rathaus is Göttingen's most famous figure. She is known as the "most kissed girl in the world" since every local student who receives a Ph.D. gives her a kiss (after being dressed up with a silly graduation hat and wheeled to the statue in a handcart).
Churches. Four of Göttingen's churches can be seen from the metal "Vier Kirchenblick" (four churches view) in front of the Altes Rathaus (James's, John's, Alban's, and Michael's). Mary's is also worth a peek inside.
Jacobikirche (St. James's Church), Jacobikirchhof and Weender Str. Built 1361-1461, St. James' has the most interesting interior of Göttingen's churches, with fascinating original paintwork (not unlike that of a barbershop) and modern stained-glass windows. The Ott organ is also impressive. It is sometimes possible to climb the tower, although the last set of stairs to the view may be blocked off - ask before paying a euro.
Johanniskirche (St. John's Church), Johanniskirchhof. Originally built around 1200, St. John's is the oldest of Göttingen's churches, although it was mostly rebuilt in the 14th century (the north-side doorway dates from 1245). The interior is plain, although one of the two towers can sometimes be climbed.
Albanikirche (St. Alban's Church), Albanikirchhof. Built 1423-1467, St. Alban's stands on the site of an earlier mission chapel. Hans von Geismar painted the altarpiece in 1499, and he added himself to the scene of Mary's death as the 13th apostle.
St. Michael Kirche (St. Michael's Church), Kurze Str. Built 1787-1789, St. Michael's was Göttingen's first Catholic church after the Reformation.
Nikolaikirche (St. Nicholas's Church), Nikolaistr. An English Catholic mass is held here every second Friday at 7PM. The area around the church is also used for flea markets on weekend mornings in the summer.
Marienkirche (St. Mary's Church), Neustadt and Groner-Tor-Str. The church bell tower used to be the gate into the neighboring city Neustadt (new city), which Göttingen bought in 1319. St. Mary's is probably older than that; it was formerly the church of the Teutonic Knights. The altar triptych was carved by Bertold Kastrop in 1524.
Georg-August University. The university is actually spread out in many sections around the city, though you see a couple of its buildings (the Auditorium and Aula) on the self-guided tour. Former staff and students include Gauss, Riemann, Dirac, Bismarck, Oppenheimer, Born, Hilbert, Teller, and Weyl.
Botanical Gardens, access behind the Auditorium at Weender Str. and Nikolausberger Weg. These gardens, established in 1736, are well worth a visit for plant-lovers. The former city wall around the Altstadt (old city) is also a circular green area, popular with joggers. Gauss's grave is on the southwest side.
Synagogue Memorial, Obere-Masch-Str. and Untere-Masch-Str. This memorial, designed by Corrado Cagli in 1973, stands on the site of a synagogue that was destroyed in 1938. The names of Göttingen's Jewish residents who were murdered during the "dark time" are listed below an abstraction of the Star of David.
Half-timbered houses. Since Göttingen was not bombed during WWII, it still has many original buildings. Particularly impressive are the 1549 Schrödersches House (Weender Str. 62), the 1497 house at Paulinerstr. 6, the 15th century Junkernschänke (corner of Jüdenstr. and Barfüßerstr.), the 1536 house on Barfüßerstr. (between Jüdenstr. and Weender Str.), and the 16th century house at Groner-Tor-Str. 28, which was only recently revealed beneath a thick layer of plaster. (Half-timbering was regarded as unfashionable from the Baroque era into the 20th century, and many beautiful old buildings have only recently been discovered.)
Pick up a schedule in the Tourist Office in the old town hall. The symphony orchestra is impressive for such a small town.
One of Göttingen's public swimming pools, Badeparadies Eiswiese, is a roughly 20-minute walk south of the city (or a ten minute bus ride on line 4 or 14). But if you enjoy the water, they offer a plethora of swimming pools (indoor, outdoor, large, small, hot, cold), saunas, jacuzzis, and solaria.
The Göttingen forest (follow Herzberger Landstr. east) is full of pleasant hiking trails, as well as the Bismarck Tower, which you can climb for a gorgeous view in the summer (though you may need to ask directions, since the tower is hard to find).
Cinemaxx. A cinema on the back side of the train station. They show contemporary movies mainly in German (no subtitles).€7-10. edit
Weender Str. is the main pedestrian shopping street, cutting north-south through the middle of the old town. In addition to the regular stores, there are often vendors out in the street, selling everything from jewelry to bowls to handmade furniture.
The weekly Wochenmarkt is on Tuesday, Thursday, and Saturday mornings; look for signs into the square from Kurze Str. or Lange-Geismar-Str. It's the best place in town to buy local produce from Göttingen and the surrounding region. (Addendum, July 2008: Perhaps this should say "the second-best place", as today there is a health food store within the old town walls (and a second outlet just a few blocks to the east) that sells organically grown produce - and a lot of what you find there is gown by the people who run the store, and may have been picked that same morning. Boyer's Heath Food Store (Bioladen), Burg Strasse, between Friedrich Strasse and Theater Strasse. --> Added by a satisfied customer.)
In December there are two Christmas markets, one small one outside the train station and the other sprawling from the Marktplatz area to behind the old town hall and St. John's Church. You can buy a variety of traditional German gifts, mulled wine (Glühwein), and German foods.
Cafe Botanik, Untere Karspüle 1, 49-(0)551-2502858. This Persian cafe has huge bowls of spiced tea and delicious yogurt dips. The breakfasts are traditional German, not Persian.
Cafe Cortes, Kurze-Geismar-Straße 27, 49-(0)551-48159.Mr. Cortes learned patissier in the french Suisse. Splendid cakes and pralines without the ritzy atmosphere of Cron & Lanz.
Cron & Lanz, Weender Str. 25, 49-(0)551-56022. The place for delicious Kaffee & Kuchen (coffee & cake). One of the grand coffeehouses in Germany.
Da Claudio Eiscafe, Ice-cream, Lange-Geismar-Str. 39 and Goethe Allee 25, 49-(0)551-5177452. Delicious Italian gelato for a euro.
Döner. Ask anyone in Göttingen and they will recommend their personal favourite of the many Döner kebab shops in the city. Perfect after kissing the Gänseliesel and visiting the Johannis church is the City Döner (Johannisstr. 1), which is an insider among students, and Euphrat (Düstere Str.), which has the cheapest Döner in town (€1.50).
Einstein, Kurze-Geismar-Str. 9 (opposite the Junges Theater), 49-(0)551-5085725, . The new bar has an opened terrace, which is one of the rare sunny places on nice warm summer evenings.
Maharadscha, Gartenstr. 25, 49-(0)551-4886125. Good Indian dishes.
Nudelhaus, Rote Str. 13, 49-(0)551-44263. Although the sign might lead you to think it is Asian, the noodle dishes here are more Italian-inspired. The Biergarten is wonderful in the summer.
Restaurante Fellini, Groner-Tor-Str. 28, 49-(0)551-4995936. Italian food in Göttingen. (Addendum: Not bad, but Trattoria Salvatore (Theater Strasse) is better.)
Zum Schwarzen Bären, Kurze Str. 12, 49-(0)551-58284. Reasonably priced (and excellent) traditional German food. If you are only eating at once place in town (and aren't sick of German food), this should be it.
Jugendherberge on Habichtsweg, a twenty minute walk from the centre of the city, is somewhat austere and suffers from enforcing a midnight curfew; it is is, however, the only place you'll find in town where you can get a bed for the night for less than €20.
Hotel Berliner Hof on Weender Landstr., opposite the Shell petrol station, might be a more realistic option, with rooms starting at €30. It is particularly well-located for those who are in Göttingen to spend time at the University.
As mentioned above, Göttingen's location at the cross of two ICE train lines makes it easy to reach most other major German cities. There are also a number of smaller towns that are worth a visit, which could be seen on a day trip from Göttingen. For the local trains that go to these towns, you can buy cheap group train tickets that can be used for up to 5 people: the €29 Niedersachsen-Ticket is good for all-day travel within Lower Saxony on any day of the week, and the €40 Schönes-Wochenende-Ticket is good for all-day travel anywhere in Germany on a weekend day. You can reach any of these places on local trains in under 2 hours:
Goslar is a UNESCO World Heritage Site, with 1000-year-old silver mines and a palace.
Hamelin (of pied piper fame) has weekly reenactments of the tale on summer Sundays.