There's not much good camping in the Denver metro area, but the St. Vrain and Boyd Lake state parks might do well if you can get by with electric only, but reservations 6 months (or perhaps it's 180 days) in advance are needed if Fri and/or Sat nights are included, since they fill quickly. There's a KOA in Ft. Collins that's doable, and there are some commercial RV parks in Colorado Springs that might do well for you, perhaps the Garden Of The Gods RV Resort or the Colorado Springs KOA.
An ideal place would be at the Winding River Resort immediately adjacent to the west side of the Rocky Mountain National Park (a few minutes from Grand Lake), which is huge and has choices of full hookups, partials or dry camping, even room and facilities for horses -- it's gorgeous, but you'd probably need to take I-70 to US40 north over Berthoud pass then through Granby to get there.
I'm not sure what transportation you'd need to arrange, but other than renting cars (perhaps car pooling) there's little commercial transportation available (busses, cabs) around most Colorado RV parks, though the Garden Of The Gods RV Resort is actually in town and you might be able to catch bus or cab. Unlike some places in the east, most areas in Colorado, and much of the mountain west, aren't geared to mass transport outside of town.
There may some folks who are more aware of transportation facilities than I am -- hopefully they'll chime in -- but you might help by indicating exactly what kind of transportation you're thinking of.
