Summit County/Eagle County has miles of "sedate" paved - but challenging bike paths - extremely popular in the summer, but also extremely gorgeous.

There are a number of mtn biking trails of various difficulties leading off of the paved trails, some very challenging - for your sons - not you. Keep in mind that you are STARTING at 10,000 feet in Breckenridge. Also, depending on the time of year there may be a number of riders who have rented bikes at one of the seemingly over one thousand bike rental shops in Frisco, Copper, Silverthorne, Dillon, Keystone, Breck (what they call Breckenridge), Vail, Eagle who haven't a clue about how to ride a bike - i.e., signaling, stopping flat-dab in the middle of the trail to fix the crying baby in the trailer, etc., etc.

But, still, one can have great fun. It will be cold at night, and can have a rainy short thunderstorm any afternoon (and this is cold - near snow/hail rain, not warm mid-western rain). Layers.

One of the favorite activities is to bus a bunch of folks and mtn bikes to the top of Vail Pass and turn them loose for about 15 miles of - sometimes - steep and curvy downhill. Accidents happen. Being of the "old school" I think that one should earn the right of a downhill by doing the uphill first, but I have apparently lost that argument.

But, mostly, the high country is a ball.

They have a plethora of free mtn biking brochures with - maybe - fifty various mtn biking trails in the area. Do some googling.

http://www.mountainbikecolorado.com/?q=summitRides

and much more