Is there a server that aggregates accommodation offers (not necessarily only) for the Italian Alps? I mean something like Tiscover (which is mostly Austria focused and has very few offers for Italy). Since I am a bit on budget the server should allow to sort by price within a reasonable radius around destination (like Tiscover can).
I don't know of others big aggregators for northern Italy. Many hotels and B&Bs have their own website with prices published there, so you can try a Google search with hotel + name of the place where you want to stay.
If you plan to stay more than a week in the same place, maybe a tourist accomodation would be better.
Prices start from about 300 - 350 euro per week, I don't know if it fits with your budget.