I'd suggest planning an extra day in case of rain; even LA and San Diego get an occasional day-long rain, and traffic is a mess then, and ... do you really want to sit in a hotel room for a day watching it rain?

I'd forget anything in the north, if you want to fly straight in. If you can allow 2-3 hours for a connecting flight, places like Tucson or Albuquerque become possibilities. Direct flights (without looking anything up): Atlanta or Charlotte? Chance of cold, snow or rain, are too high. Miami, Dallas? Fair to middling weather chance and road cycling. San Francisco? Nice cycling in the area, fair chance of good cycling weather. Los Angeles, San Diego, Phoenix? Pretty good chance weather-wise, good cycling available, especially with a rental car drive.

I'd suggest double-checking winter hours for rental bikes. A lot of places are closed on Sunday, presumably when you'd want to drop the bike off and head to Vegas. You'd have to work out a way to get the rental bike back to the shop ahead of time.