A couple of things to work from--bear in mind, though, this is from someone who has not been there in a long time. But you never forget it.
1. Investigate campgrounds on the west side of the park. The east side is great, spectacular, unbeatable...but it's also where everyone else is. Look for something to the south of the Never Summer Range, maybe around the Shadow Mountain Lake area (I think Grand Lake is probably mobbed).
2. On the east side, consider the YMCA complex that is between Estes Park and RMNP; they used to have regular--several a day--hikes of varying levels of strenuousness. Of course, there are some Park-organized hikes, and there's plenty you can do on your own, but if the Y is anything like it used to be, they're great for organizing things to get you acclimated (and don't underestimate that--if you are from lower elevations, being a mile and a half above sea level is quite a change, and you can easily mess yourself up by taking things too quickly; but there are things you can do to prepare during the month prior to your stay, wherever you are from).
3. Don't neglect the area south of the park, known as the Indian Peaks wilderness area or something like that. RMNP is great, and nothing beats Long's Peak, but there's some scenery and trails in the Indian Peaks that are really spectacular.
4. Wish I were going! Enjoy it, and go back next year and the year after that. It never gets old. Like Yosemite, Yellowstone, the Grand Canyon, Bryce Canyon, and a dozen other parks, you could spend your entire life there and never get tired of it.