Well, crawfish season starts right about now, so you should see some boils happening at various restaurants around town. I'd call places like Evangeline, Shoal Creek, and The Original Po Boy and Gumbo Shop trailer (on S.Congress) and ask if they're having any in the near future. It's not a regular menu item at most places, more of an occasional event. I'm sure if a place has a boil, they'd probably sell you some takeout.
Also, though I've never been, there's Hot Boiled, the Vietnamese crawfish place. I don't really know anything about it, so I can't vouch. I've always wanted to check it out, though.
Aaaaaaand this might sound annoying when you just want takeout, but being from the Mississippi/Louisiana region, I've gotta say that your best bet is to cook them yourself. You'll probably save a lot of money, and all you really need is a burner, propane, a big pot and some Zatarain's crawfish boil. Boil crawfish in your garage, drink beer, be happy. Plus, you can use the same setup to fry a turkey :)