In the US, what can be done at an airport when volunteering hours?
Commercial airports are challenging for volunteers because of security, if you want to do anything beyond the security barrier (ie where the interesting stuff is) then you need to be cleared and supervised, and that costs time and money. 

There may be opportunities at small airports, which don't have the same security concerns. Most won't have any established volunteer positions, it would be more of a case of talking to the airport manager or someone running an FBO and asking if there's anything you could volunteer for. Ask politely, wait a few days, then follow up with a phone call, if they know you're genuinely interested (and polite, sensible, not likely to run into a propeller) they might be willing to offer something to you. 

One last thing, if anyone asks you to get a bucket of propwash it's an old aviation joke.