Aurora runs north/south along the far east side of the Denver area. The Summit county areas and Winter Park are about 80 miles from the north end (I-70 & I-225), and Vail another 25 miles. Commute times to skiing will vary depending on when you travel - if you leave at 6:00AM it will be 1.5 hours, if you leave later it could double. As you go further south the times will increase another 15- 30 minutes as you approach Parker on the south. If you lived on the west side, say near Golden, you could cut a half-hour, but the daily commute to Aurora would be in the 45-60 minute range.
Water based recreation, such as it is, is limited is mostly on the east side with Cherry Creek and Aurora Reservoir. Mountain based activities such as mountain biking and hiking are on the west side. If you are going to play everyday on the west side, the long work commute be worth it. Tough choice.
Some east Denver areas you might want to consider would be the Park Hill area, older, smaller homes in what was once a country club type setting. Just to the east of there is a new development at the old Stapleton Airport (I-70/Quebec)now closed), it is being done in an old-style neighborhood format. South of there is a re-develpment of an existing neighborhood and former air base called Lowry (Alameda and Quebec). Anything east of I-225 will be mostly suburban. The general area of Aurora/East and Southeast Denver has a great diversity of housing, styles, and neighborhoods. You should be able to find something that suits your needs. If you are renting, you only have to live there for 6 months to a year, if you are looking to buy you may want to rent for a few months to get the feel of the area. Note that Aurora has very strict watering restrictions, if you are into gardening, or think you will miss that New England green, Aurora might not be the place.
Commutes from Aurora can be bad along I-70 east and west bound, major west bound routes into downtown Denver, and routes into the Tech Center, which includes Parker Road Arapahoe Road and I-225. If you can travel against the rush, great!
School Districts in that area are Denver (poorly rated), Aurora, Arapahoe, Cherry Creek (highly rated), and a little futher south Douglas County (highly rated). Google for "CSAP tests" in Colorado for very detailed info on schools.
Hope this helps, feel free to PM me if you wish. Good luck and welcome to Colorado.