There's a world's largest flea market/rock show/etc. in Quartzite in the late winter/early spring (February/March). Quartzite is on I-10 between Phoenix and the California border. It's well worth stopping for a few hours -- you never know what you'll find, and the people watching is amazing.
Phoenix has a Renaissance Faire that is a bit hokey, but worth attending for fun, in the late winter/early spring.
You can drive to the top of South Mountain, the big mountain south of Phoenix, and some neat trails. There's also a riding stable at the base that has trail rides. It's worth the drive to the top, but again, leave your trailer somewhere -- don't try to drive rig up to the top of the mountain. It's a very narrow, twisty road and there's not a lot of places you could turn around. If you do drive up it, I recommend timing it see the sunset and the city lights at night.
If you want to go a bit out of the way and don't mind mildly chilly temps in winter, Wildlife World Zoo in Camp Verde, Arizona (a couple hours from central Phoenix depending on traffic on I-17), is WELL worth the price of admission. It's a bit of a different zoo than most -- the animals are in large enclosures on acreage. They also have a big cat show where the zoo staff play games in an enclosure with lions and tigers that's worth watching -- the cats look like they're having a blast, and so far, they haven't killed any of the staff, LOL. If you venture up to Camp Verde, you might also see the sights in Sedona, go antiquing in Clarkdale, and definitely drive up to Jerome. (Just drop your rig somewhere -- you DO NOT want to try to take a rig through Jerome!!!!)
The tourist train from Clarkdale up the verde river canyon is worth the price of a ticket, too -- especially if you can afford first class tickets. It goes through a wild and remote canyon, and you are very likely to see bald eagles, hawks, and assorted other wildlife. DRESS WARM as the wind can be quite cold.
Do be aware that it's possible to be stopped by the cops in southern Arizona, particularly on I-10, Maricopa Road (Hwy 347), and I-8. Drug and human smuggling from Mexico is a major issue, and for obvious reason, travel trailers -- or any trailer -- are objects of suspicion. The cops may make up a pretext to pull you over -- they often told me that I had a "brakelight out" and my brake lights would be fine later. (I drive a beat up pickup and always seemed to get pulled over when I had a load of hay bales in the truck. I figured they thought I might be hiding pot under the hay.)
Just bear in mind they're NOT looking for you and they aren't interested in harassing genuine tourists. Arizona likes tourists! *grin* They're really looking for the guy who's got two tons of weed or a couple dozen illegal immigrants hidden in his rig. If that's not you, you'll be just fine. The best way to deal with them is to just relax, smile, be friendly, follow their orders exactly, and make sure your paperwork's in order and your rig is properly hooked up. (Brakes and lights connected, etc.) You may find a rude/curt cop occasionally, but I've yet to run into one who's been abusive of his power beyond making up an excuse to pull me over in the first place.
(The smugglers themselves won't bother you. They don't want to make trouble -- they want to fly under the radar and not be noticed.)