Also consider starting from the West side of the wilderness area. Excepting holiday weekends, I haven't found either side to particularly crowded. I just prefer the west side because it is more convenient.
From the Monarch lake trailhead, it is possible to do a couple loops. The Buchanan pass/Pawnee pass loop can be done from that side, though it adds another ~3 miles or so. From Monarch Lake, you can also hike up to caribou lake > Arapaho pass > caribou pass > Caribou trial > High lonesome trail back to monarch lake. From the Columbine lake trailhead, it is possible to do the same loop or the Devils thumb loop previously mentioned.
I hiked the caribou lake loop last summer over the weekend of July 4. There was still TONS of snow, and we had to use snowshoes for most of the terrain above 10,000'. Following the trail was pretty impossible with 10' of snow on top of it. This year shouldn't be nearly as bad.