Wells fArgo, 1st bank, US bank are 3 big ones. There are others. Tons of restaurants. In Avon theres some decent apartments called buffalo ridge that are $1000/month for a nice 2 bedroom with a garage. Just look at craigslist/high rockies for more exmples or vaildaily.com
I'm in an all bills paid condo on the river in vail, 2 bedrooms and higher end finish interior for $1700/month there are places for $1000 if you keep your eyes open but you have to look between June and sept/oct or the prices go a lot higher. Frisco and silverthorn in summit are nice and relatively inexpensive. If yo go down to eagle it's a lot less but 30 min to vail, 20 to beav.
There's free buses within summit county, within vail and within Avon. There's an eagle county bus but it's a little $ to ride, most businesses give free bus passes for the eagle county bus though.