It's roughly 90 minutes from everywhere in the Denver Metro to the Front Range Ski areas. Loveland, A-Basin, Copper, Keystone, Breck, Winterpark. Give or take 10 minutes. Vail/Beaver Creek puts you at about 2 hours.
I have no idea what the rents around Westminster are going for, but I'd say expect to shell out $100-$200 more for a similar place. I'm sure you can find rents at the same price, but the accommodations probably suck.
All that said, look for a place close to your work. If you want to be in Denver (probably the best spot for a young guy), North to Northwest Denver is a good area to look. Check out spots around Regis University. The Tennyson neighborhood is pretty sweet. 44th and Tennyson puts you in the middle of it. Probably some reasonable rents within 20 blocks of that area. Gets more expensive the closer you are of course.
Westminster is a nice enough town. Very much the 'burbs, but it is close to Boulder and all that area offers (world class rockclimbing, mountain biking, hiking, college girl watching and/or stalking...). Being close to your job is always nice.