We've rented from http://cycletucson.com/ with success a couple of years ago (now we have S&S coupler bikes that travel to Tucson with us each winter).

For locals Feb may be cold, but even though we've seen snow some years, it is [almost] always warmer than home. One year we had a miserable first day -- heavy rain with temps in the high 30s (temp would have still been better than home but with the rain....<shudder />). But we also had some lovely days in the 70s that trip. So we still considered the trip worth it.

Definitely make sure the bike has a flat repair kit. You will need it.