I honestly don't know if they still do that; but, I stayed in a barracks at Andrews AFB when my Jamboree Troop stopped off to tour Washington, DC, in '77. I subsequently stayed in the VOQ (Visisting Officers' Quarters) some years later, though I was a low-ranking Senior Airman at the time.
Anyhow, call the base Public Affairs office (301) 981-4424; give them the details and tell them what you want (billeting for your group). You may also want to try Billeting directly at (301) 981-4614. The Base Operator's number is 301-981-1110. Don't underestimate the folks at switchboard; these folks will know how to navigate you to the right office. If you're successful, I expect you'll also need to contact Pass and Vehicle Registration at (301) 981-0689. (Be advised, all four of the above resources are funtions of different squadrons, if you know what I mean.)