Here is alist of hostels and hotels in Trento ordered from very expensive to relatively cheap. Alternatively you may want to trust this Google search.
When you look for an hotel, check out its location: it may be near to a bus stop of routes 5 or 13, which will drive you directly to the FBK, see How To Reach the Fondazione Bruno Kessler.
Here you will find a somewhat crippled map of the bus lines in Trento city center.
Note