In the Colorado Springs area, we like the state park campgrounds. Cheyenne Mountain State Park is very close to the city, Ft. Carson, and the Cheyenne Mountain NORAD Tunnel (if you get tour reservations well in advance). It doesn't have large trees, but some sites are well-screened by small trees and bushes. It has 32 FHU sites if you are planning to stay for a while. We stayed there during the Colorado Springs Balloon Festival and had a great nighttime view of the city from our rear picture window.
Farther from the city, but a state park with a spectacular mountain setting, is Mueller State Park on CO 67 between Divide and Cripple Creek. No FHU sites area available, just tree-shaded, 30/50A electric sites with separate water and a dump. This is one of Colorado's most popular state parks, even in the fall, so reservations are a must.
Both parks are open year-round and reservations are available on ReserveAmerica
HERE.