I would recommend Java, Rue Marterey 36, which is close to Rue de Bourg. The ambience is great, the food fantastic, and the prices are very reasonable considering the quality. It's good for visiting guests as well because the food has a definite French flair. They specialize in crepes (the savoury ones are called galettes), but they do fantastic salads as well (I highly recommend the warm goat's cheese one. I could eat it every day and never get tired of it!)
You can check out the menu, prices, etc. on their website.
http://www.lejava.ch/
Reservations recommended.
For a very Swiss experience, I'd recommend grabbing a roesti or fondue with them at La Pinte Besson, Rue de l'Ale 4, which is in the middle of town. It's the oldest pub in the city and has a great atmosphere (complete with the regulars who come every night and sit and the bar and drink wine. I always seem to end up deep in conversation with them at the end of the night.

) I'd recommend going in the middle of the week: because it's so small, it becomes very loud and smoky when the weekend crowd comes in. There's no harm in reserving a table.
http://www.pinte-besson.com/
Bon appetit!
HeatherM