I live in Denver. You have access to like 100 mountains but it can be a drive, especially if you get stuck on I-70. I found a group of buddies that ride and we've rented a condo 10 min from Breck, Keystone, Copper, and about 30 minutes to Vail and Beaver Creek. We each pay <$150/mo.
Denver has a solid music and entertainment scene, great places to skateboard, and Boulder is 20 minutes away for all of your extracurricular... needs...