The Rim Trail is a popular intermediate hiking and biking trail that follows the ridge line that makes up the west edge of Brush Creek Valley where Snowmass Village sits, and goes all the way from Ziegler Reservoir in the south all the way to the Snowmass Rec Center and Rodeo grounds in the north for a total of 7.9 miles and has free busses that can take you to both ends. The trail has great views of the town of Snowmass to the east, the whole Snowmass ski area to the south, and Wildcat reservoir to the west. And you can see several Colorado 14ers including Capital and Snowmass peaks
View of Wildcat Reservoir
The trail is evenly broken into North Rim which is 4 miles and 600 ft elevation gain, and South Rim Trail which is 3.9 miles and 1,000 ft of elevation gain (although before the road cut was put in, you can see that it was one continuous trail). Instead of taking the whole trail, you can start or finish at the Rim Trail juncture at the top of Sinclaire Rd where there is parking. The North Rim Trail is closed from Dec 1st through May 16 for elk migrations and calving, but you can find the cache year round (you might have to dig if there's been a recent big snowfall).
Both summer and winter hiking/biking/horsebackriding trail maps can be downloaded at the snowmass website.
http://www.gosnowmass.com/about-us/maps-travel/snowmass-trail-maps/