I'll Play !
Every "so often" I'll use the air compressor, outside with some cardboard slid between the bike and chain, and literally "clean" the chain that way. Spin the chain backwards and hold the spray nozzle right up close to the chain. Wipe, repeat as necessary. I consider this a "deep clean", hah hah.... as if a "dirty" chain could ever be "made clean" ... or a "clean" chain "made dirty"...... oh but that's another story.
This works for me for the conditions I ride in as I always wipe off any excess oil from the chain. I even use bulk/drip-able WD-40 as lube, or airtool oil sometimes. I wouldn't recommend it to anyone though, live and let live, do and let do ... not like there is any choice in the matter anyways .... (laughing).....
I also use the compressor for blowing off any excess brake dust, or where ever I see stuff than can be blown off. I don't do this often, only if this, when that .... you know how that goes.... "I do it as/when I do it".
Otherwise, some obvious and not to obvious outdoor uses include tires for any motor vehicles, snow blowers, tractors/riding mowers, and anything with a tire valve....power washers/tools, blowing the dust out of fans/air filters, reusable vacuum bags and anytime I want to quick dry/blow off "something" suitable for such air. Of course the pressure is adjustable on most compressors. We have an ancient one in the basement that has no adjustment.
All of this is done outdoors, for obvious reasons. The only time I used it indoor for blowing air was for a bathroom fan vent duct that went straight up. A high pressure AC leaf type blower(and I mean HIGH) also works for that, and for blowing out the buildup of lint in dryer vent tubes. Seal around the blower nozzle with a wet rag and crank it up.... weeeeee ! It sounds like Dorothy being blown up into the sky on her way to Wonderland ...... "oh we're off to the see the Wizard ..... the wonderful Wizard of Oz .....tah dah !"