It really depends on what you are looking for. Are you looking for solitude or the best scenery (hint they don't always go together). Here are some ideas for trips.
Closest to Denver.
1. Lost Creek Wilderness - There are a number of trip reports about this are by myself and others here. Lost Creek is best known for its canyons. They are great but they will be warm in August and some smaller creeks up high will have dried up. There is alpine scenery but its not as specatular as other areas. There is a figure 8 of trails so you have three possible loops: a 20 hike through mostly canyons (Good Creek mostly), a 27 mile hike that skips most of the canyons but hits 5 miles of alpine trail, or a 36 mile loop that hits everything. If you want to add even more you can go up one of several trails then bushwack along the crest of the Kenosha Mountains. Summitpost.org has info on this route.
2. Indian Peaks Wilderness - This is just south of Rock Mountain National Park. There are several possible loops across the wilderness. Dondo did a trip report on one starting at Brainard Lake. Its a beautiful area but you will see more people here. A permit is required if I recall but I don't think there is a quota. Just make sure you get it ahead of time. Its a long skinny wilderness area so getting 5 days out of it might take some creative route planning.
3. Rocky Mountain National Park - This is a very scenic but more people and more rules (designated campsites, hiking permis and bear canisters). A good thing is its a big area so getting in your mileage may be easier.
These are the main areas relatively close to Denver that I would recommend. There is good hiking near Breckenridge but its not very wild (lots of dirt roads and mountain bikers).
If you want to drive farther you might check out the Sangri de Cristo Wildenress, the Collegiate Peaks or the Maroon Bells (probably the most crowded you'll see though).
If you want to drive about 8 hours or more the Wimenuche and South San Jaun are scenic and remote.
Hints for planning
1. Look at topo maps. Look for areas that are above timberline. These will be the most scenic.
2. Download the free google earth and check out areas that sound interesting. Google earth will often give you a good idea how scenic an area will be. Popular areas like Rocky Mountain National Park often have images imbedded that you can click on to view.
3. Check out summitpost.org. Its more geared towards peak baggers but they have good info about different areas and lots of maps and pictures.
EDIT - I just remembered you like a campground near the trailhead. I think your best bet would be a hike starting at the Brainard Lake Campground at the edge of Indian Peaks. You'll have an awesoem view from the campground and the hike will be great. Its a shorter loop but you might be able to do some side trips to other lakes or bag a few peaks to extend it. Just one thing. This campground is understandably popular so you will probably have to make reservations ahead of time. They were doing some construction but hopefully they'll be finished by August. If that doesn't work there are some other good campgrounds in the area. There is a nice loop hike around Brainard Lake. You might see if your brother in law wants to hike that far with you (about a mile I think).