I think it might be important to know how to do more even if you are riding near a major population center in the US.

Over the weekend I did a ride along the Mississippi and Missouri Rivers near St. Louis MO. About 10 miles out from the last bikeshop I caught a stick in my rear wheel. Fortunately all it did was crumple the fender, but if the fender struts hadn't been there to stop the stick, it probably would have ripped out a few spokes.

If that had happened, I would have been able to deal with it because I had the tools to remove the cassette and spare spokes to rebuild with. If I hadn't had those, I would have needed to hitch hike back to the last town and hope the shop was still open (it was saturday afternoon.) If it had happened on a Sunday I would really be out of luck.

I'd say you need to know how to reconnect a broken chain, boot a slashed tire (or have a spare tire with you like I did, along with material to boot a tire), replace spokes especially on the drive side of the rear wheel, and have some duct tape, wire, etc for lashing other things back together. I forgot the wire, but I lucked out and nothing busted.

Get a book on bike repairs. Maybe something oriented towards tourists. I have Zinn's "Art of Road Bike Repair", but it doesn't cover cantilever or U-Brakes and doesn't talk about racks, etc. Maybe www.adventurecycling.org has something.