Check all of the regular rental sites every day. Good housing moves fast.
Craigslist, Trulia, Zillow, Apartments.com, Hotpads, Vaildaily.com
As you move down the valley, Avon, Edwards, Eagle, Gypsum, you get more for your money but will need to commute farther. As long as you have a decent vehicle, the drive is a breeze. The Eco Bus also goes down to Gypsum. These bedroom communities are ideal with less expensive restaurant and entertainment options.
If you want to live right in Vail, consider a roommate situation or perhaps an affordable housing option like "middle creek." These solutions are not ideal, in that you may end up living with a party animal, BUT, you will get to know what it's like to "live the vail life" for a season!