Boulder, CO – Sept 24th Weekend?

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.
http://indianpeakswilderness.org/ipwa_trip_plan.htm#Permits

In both areas backcountry traffic really thins out after Labor Day.

Indian Peaks is a great option as William said. Also James Peak Wilderness right next to it is good for an overnighter. If you're willing to drive a couple hours, Lost Creek Wilderness is nice as well. Those are my favorite close to Boulder areas to backpack.

Thanks ya'll! I've been looking at the Indian Peaks area as William mentioned. There are just so many trails in the area, and all the great photos out there make it hard to choose. We're going to rent a bear canister either in Boulder or Estes Park. Would bear spray be good insurance to have too? I think we'd like to stay at lower altitudes both to get acclimated and also because I'm not used to the weather at higher up.

I would not spend weight or $ on bear spray.