Hey, Davos is 5 different hills set around a sort of isolated valley. The town (towns) are spread along this valley and you pick which hill you want to spent the day on each day and take the Gonola up to the rest of the lifts. Public transport is exceptional (it's Switzerland) and a train line goes along the valley which you can use to get from the different centres, the different base lifts and to continue out of the valley to the main line connecting to Zurich and the rest.
On the other side of the main line (ie no longer in Davos valley), and up another valley is the resort of Flims Laax and Arosa is also near. the point is, living down near the main line in chur, or some town, should be cheaper but you would have to commute to the resorts and it wouldn't feel like a season.
Davos and the linked towns in the valley, like Klosters or Davos Dorf, combine to make a very large ski town spread along the valley floor and rent will vary away from those three main centres I mentioned.
However, rent in Switzerland is very very high and it could seem to people that this is because you are looking in a resort when, in fact, rent all over the country is severla time higher than in N. America. It would be challenging, for example, to rent in Zurich for under $2K per month and Davos is likely the same.
Austri may be cheaper, out of a resort Innsbruck is well conected for boarding.
hope this smorgesboard of info is useful.