Favorite thing: Go shopping! I've heard that Bern is a big shopping destination for many people. The good thing about the city is that even in terrible weather, snow/rain, most of the city is made of covered arcades, or shops. So you could wander around under the roofs of all the covered stores.
Loeb is a local store, where you can shop all kind of things, wear, books, gifts. Window-shopping is really original there, it seems like there would be always new ideas. So just have a look, it might be funny...
It's near the main station of the railways SBB
Meeting point Nr. 1 in the city is the Loeb Corner.
Favorite thing: Keep a look out for these lovely arcaded through-ways. There are many of these arcades that allow you to switch streets without getting caught in the rain or traffic.