I have found that most bike shops will accept your bike if you arrange ahead of time. Ditto for boxing and shipping a bike home at the end. You might also ask Warmshowers.org hosts in the area or if you plan to get a room you might ask the motel/hotel.
I usually like to ride out of the airport so I typically fly with my bike as checked baggage. If you do that, fly with a bike friendly airline. Southwest is usually my choice ($50 for the bike and no other baggage charge if you keep it to the bike and one checked bag with each being under 50 pounds), some other airlines charge as much as $200. I typically like to have a bike shop ship the bike home for me to avoid having to deal with that in a strange city.