Bern, Switzerland

Bern is the capital and the fourth most populous city in Switzerland (it's smaller than Tampere!!) The city center is largely medieval, built on a narrow hill surrounded on three sides by the Aare river. The Old City is home to Switzerland's tallest cathedral as well as other churches, bridges and a large collection of Renaissance fountains. (Wikipedia) Public transport works well there and InterRail passes are valid on the S-Bahn so getting around shouldn't be a problem.

Places to see:

• Bundeshaus (the Federal Palace): houses the national parliament, government and part of the federal administration. There is also a set of fountains in front of the Palace.

Bundeshaus

• Einsteinhaus: a museum and former residence of Albert Eistein, who worked out the theory of relativity while living in Bern. The living conditions of Einstein and his family are shown accurately in the apartment on the second floor with furniture from that time. Einstein’s biography and his life’s work are presented on the third floor.
• Zytglogge: a landmark medieval tower, built in the early 13th century. Over the years it has served the city as a guard tower, prison, clock tower, center of urban life and civic memorial. The tower is one of Bern's most recognizable symbols and its 15th century astronomical clock is a major tourist attraction.

Zytglogge

• Münster of Bern: the tallest cathedral in Switzerland. The bell tower is open to public - the lower platform (254 steps) offers views of the entire city and on a clear day even the Alps; to reach the higher platform there is an additional 90 steps to climb.

Münster of Bern

• Untertorbrücke: a stone arch bridge, that spans the river Aare - the oldest bridge in Bern. Its construction was completed in 1489, although it has been renovated several times since then.
  
• Fountains: the city of Bern is known for its 16th century fountains designed by Hans Gieng. There are over 100 public fountains in the city of Bern of which eleven are crowned with Renaissance allegorical statues. This one is particularly good, in my opinion. No no, you're not mistaken, it really is a sculpture of a man eating babies:
  

The Kindlifresserbrunnen

• Rosengarten: little park with a splendid view over the old town. Can be easily reached by bus number 12 from the railway station in Berne in direction Zentrum Paul Klee.
• Gurten Hill: The Gurten is a lovely hill just outside the city. It features a park and great view over the city on one side and a nice panorama of the Bernese alps on the other. The park is visited heavily by locals to play ball, to barbecue or to just lie in the sun. Tourists are not an unusual sight, though this little attraction is missed by most of the many that visit the city. A wooden look-out tower allows an even better panorama than that you would already have. The Gurten can be easily reached with tram number 9 from the railway station in Berne in direction Wabern. (Wikitravel)
  
• Apparently the bear pits (bärengraben) is currently empty, but there is a bear park (bärenpark) as a replacement. It is situated near the Aare river. If I understood correctly, it's free to visit the bear park - only the guided tours have an admission fee.

Where to spend the night:
Just like in Zürich, hostels are roughly 35-40 CHF/person/night. There is Hotel Glocke, which is right in the center of the old town and a Youth Hostel also in the old town.
Camping Eichholz is not too far from the city and costs 7.50 CHF/person/night (or 6.50 CHF, if they accept our student cards..) Finally, there's Camping TCS Bern-Eymatt, but I haven't had the patience to try and make sense of their website yet, so I don't know if it's any good.