Just grab a map and start looking at medium-sized towns, I pretty much guarantee they're snowbird cities.

Yuma, AZ is pretty big that way, so is Casa Grande AZ. Apache Junction, AZ may have never seen an Apache indian but sees lots of snowbirds! I name these because they're also decent cycling - Yuma has a regular snowbird-cyclist club now, Casa Grande has a brevet series and AJ is good riding too. As long as you don't get run over by a snowbird
Marana, AZ is also an honorable mention, partway between Casa Grande and Tucson. There's a big spring ride there that goes around the Tucson mountains, it's worthy!

Prices don't spike all that much, I don't think. Housing / hookups for the RV are about the only pressure point I know of.