A few other ideas to toss out (I'd still recommend RMNP - on weekdays it isn't too bad and it's an amazing place).
- Mount of the Holy Cross (just south of Vail). This is fun/different as you get to knock out a 14er as part of it. Hike in about 3 miles to one of the prettiest little stream valleys I've been in. Stay the night and summit the 14er (Mount of the Holy Cross) the next day. Then, hike out. It isn't as long as you wanted, but is a bit more strenuous (doable by most, though). There are definitely other folks there, but with a hammock, you can get out of the way of others (everyone congregates to a few obvious tent site areas).
Major downside is that as far as I could tell, there were 0 fish in the stream running through the valley. The views of the area were unreal, though. You can always fish near Eagle or other similar places nearby.
- Eagles Nest: Hike from Green Mountain Reservoir (just north of Breckenridge area) up a trail to a series of lakes. Hike as much or as little as you want - 5 or 6 miles to the first lake. Good fishing and good hanging.
If you're interested in details on either PM me and I'll track down some info links.
Father. Husband. Scoutmaster.
Eagles Nest is a great area!
BTW, don't be too alarmed at the elevation gain and the "Advanced" rating. That rating is really more about the length (distance) of the trail. It is well switch-backed and a slow steady pace gets you there just fine. You'll find lots of spots you'll want to stop and look around anyway. Just be aware of the altitude you'll be hiking/sleeping at if you chose to hike it. The lakes are right around (or a little above) 11,000'. Be VERY well hydrated.