My wife and I are going to be retiring in the next couple of years and would dearly like to get out of Western Washington for a few weeks in Jan and Feb. We have thought about Phoenix or Tucson but I know those are bigger cities. Are there places around the area that aren't as crammed with people? What about New Mexico? Are Prices dramaticly (sp) higher during that time of the year?

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.

That big spring ride is on April 27, Tour of the Tucson Mountains, starts and finishes at Marana city hall. Choice of 27 or 76 miles.
Check perimeterbicycling.com
Lots of good riding in the Tucson area and city itself boasts over 400 miles of bikelanes.