There are lots of places to see and go in AZ during the winter. Finding a spot in a established National Forest or State campground can be a challenge due to the popularity of the state during the winter months, (just like you, many others are coming for the weather) but a smaller RV like your's shouldn't have much problems if flexible in dates.
In addition to all the traditional private, County, State and Federal campgrounds, AZ is loaded with open lands under the BLM plus the added advantage of large tracts of Arizona Trust Lands that are also available for dry camping.
Probably the best way to start is to outline your interest and desires for when you visit. You can have everything from a vast mountaintop secluded spot overlooking a valley with photos you'll never forget, but if you want the tourist thing with yee-ha swing dancing and staged pow wows, that's a different recommendation.
So is it the Mount Graham experience, the Tombstone experience, the I'm glad I saw this experience or the do nothing but talk over pot luck meal experience?
1994 Itasca SunDancer 21RB - Chevy G-30 chassis.