Going to be hard to get away from people if you're talking about Rocky Mountain National Park and/or the town of Estes Park specifically. Estes Park is a tourist trap with not much more than restaurants and junk shops and is always crowded. Don't get me wrong, it can be fun to see and walk around, but it isn't a quiet mountain town.
RMNP will be on timed entry...reserve as far ahead as possible and make it for as early in the morning as possible unless you want to sit in line in your car for, and I'm not exaggerating, hours. I have seen those lines stretch miles down the road.
All of the stuff
@270-300 mentioned is far enough away that they aren't day trips from Estes so if you have lodging in Estes I wouldn't plan on any of those unless you can plan to stay the night at the destination.
If you are staying in Estes and want to avoid the larger crowds to hike and fish I would head towards Glen Haven/Drake out of Estes and find some trails. If you head east out of Estes on 34 there's plenty of holes to fish along the Big Thompson river.