Denver has an extensive MUP system. There's one down-loadable map here:
http://www.denvergov.org/Portals/708/documents/Bike_Map_Final_2012_Final.pdf
There's also a pretty extensive light-rail system that you can take your bike on. Some rides to google:
Deer Creek Canyon (with or without High Grade Road) - accessible from downtown via the end of the SW light rail line or via MUP
Lookout Mountain (with many options thereafter) - accessible from downtown via the "W" light rail line or MUP
Golden Gate Canyon - also from the W line or MUP
There are also a number of Jefferson County Open Space parks (Apex, Mathews-Wiinters, White Ranch, Mount Falcon, Green Mountain) around the town of Golden with extensive dirt trail systems suitable for a cross bike. All are accessible from the W line (or MUP) from downtown.
You should be able to find lots of info based on this and some google searching.
Have fun!