I seem to remember many years ago when I came to RMNP for some backpacking that I stayed up in Lumpy for a night. I had finished up the loop in RMNP proper, and then wanted another night nearby and that was suggested by a ranger. I could be totally off base there though, because that trip was at least 10 years ago, before I even moved to CO.
There is the McGregor Mt. site beyond Sundance up into Black Canyon, and Rabbit Ears site (good single pitch crack climbing IN CAMP) around the backside of the Ridge starting from the Cow Creek TH. I guess you could use these as a base for climbs, but they're out of the way and by the time you pay your $20 for a permit you're better off just walking in every day.