I'd second Dakota Ridge
and add Clear Creek RV Park
. Both are in Golden, about 25-30 minutes west from Rose Medical Center. Clear Creek is on the creek so it feels more like camping to me. Another idea, just south of Denver would be Cherry Creek Reservoir
. I think it is a little closer to Rose. Also Prospect Park
it's easy-on, easy-off I-70, about 7 or 8 minutes closer to Denver than Golden, but it's located in a more city-like setting - right on a major street (across from a truck stop). It does have nice facilities - but the surrounding area is not for the outdoorsy.
My two top choices to combine camping/vacation & accessibility to Rose Medical Center would be Clear Creek RV Park or Cherry Creek Reservoir.
Denver-proper doesn't have many other camping opportunities that I would consider. Happy birthing!