There will be a 3.5 room flat available in Steigerhubelquartier (Ausserholligen) Bern from April 2009. The house has 6 apartments in total, and was built in 1920 but was renovated in 2000. Original features were kept.
It's on the 2nd floor, plenty of built in cupboards, wood floors in the bedrooms, tiles in the hall, bathroom and kitchen, the house has a large garden which everyone can use. The area is quiet, two buses (13&14) nearby and plenty of train connections. Lots of families live in the quartier and there is a Kita, a kindergarten and a primary school all within walking distance. The only stipulation, as it is a Stadtwohnung (rented out by the city and not privately), that you would need to have lived (registered) in the city of Bern for 2 years. The flat hasn't been advertised as yet but the current renters have to leave by January 2009 - correction, they received an extension as their new place won't be ready by then, so the move in time is now end of April.
I live in the same house, so if you need anymore information (how to apply etc) please let me know. It is really a good, no fuss place to live, we have no problems with neighbours, noise or rules as everything is decided by the people in the house. It's also 10 minutes from the centre of Bern.
The rent is decided on income so it is between CHf 870.- and 1'100 (including NK). Still a good deal for an apartment in Bern!