The Denver area seems to have very few campgrounds in town. However, we stayed at one that is beautiful, Chatfield Reservoir/State Park.
Chatfield is just below the foothills in southwest Denver. Spaces are spread out with lots of open areas, with grass and a some trees, picnic tables, BBQs and firepits, with full hookups. There are also recently renovated bathrooms, showers and laundry facilities; and it's very secure.
This state park is pretty close to most of Denver, and conveniently located near the freeways (but far enough away to avoid any noise). I think it is actually in the Littleton city limits, but it feels like you are farther out of town.
See exact location in Google Earth using these coordinates:
Chatfield State Park (RV Registration Kiosk): 39° 32.295'N 105° 3.939'W
Camping at Chatfield | Colorado Parks and Wildlife