Upvote:2
Have you tried the classic websites like:
AirBnB
Booking.com
Hostelworld
Associazione Italiana Alberghi per la GioventΓΉ (membership card needed, 2 euro yearly fee)
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.
Media Vacanze
Prices start from about 300 - 350 euro per week, I don't know if it fits with your budget.