Depends on where you want to go. If you want to go to Glacier Gorge, the Loch, or Andrews, those are pretty hard to get on short notice. I would look at the Backcountry sitemap on the RMNP website and make a few choices, then call the Backcountry Office at 970-586-1242 to see what's available. You can also show up at the BC office when they release the unclaimed permits at 10AM everyday, and make your choice then. Keep in mind you have to have a bear cannister for camping below treeline in RMNP that time of year.
Another alternate choice is Indian Peaks Wilderness west of Boulder. The Summer permit system ends Sept 15th., after that you don't need one.
In both areas backcountry traffic really thins out after Labor Day.