This time of year, I'm heading to the lower elevations of southern/central Arizona myself, and think it's within the max drive time you stated. Hopefully the coffee-fueled travel essay below isn't too much info but I'm putting my thoughts together for my own AZ/SoCal 2+ month trip starting in a few days. Being no longer local to AZ, here's a traveling backpackers perspective after driving 5-7 hours ... Hope the central AZ locals chime in with some updates and their recommendations. So if I were coming in from I-10 after a long drive ...
East Saguargo NP's Tanque Verde is a pretty nice hike and hopefully I'll be returning there in a couple days. The NPS required starting by 10 AM and the gates were locked overnight (guess I need to check on that). Pretty unique views and I could easily do a 4-day "in-and-out" hike.
The Catalina Mtns are USFS mountains just north of Tucson with a lot of vehicle access. Lots of unique views but eventually it's getting deeper into a canyon. It still may be deer season and I remember a few Thanksgivings ago, hearing the sound of high powered rifles all over the place. They have a ski area (Mt. Lemmon), so you may also need to check any snow report. There's no overnight camping in the west Sagauros, and I have yet to explore Patagonia or Yuma (only done some "drive-bys").
I've done a couple 3-day hikes in the Superstitions with Reavis Ranch, and then the unofficial Reavis Falls (kind of a "Y" hike). I'd like to spend a little more time from Reavis for a 5 day linear or lollipop loop. Liked the hike so much I've done it twice. I've never been to Peralta but my buddies tell me the parking lot is crowded, especially on the weekend. Still that's more desert-like with waterholes (I hear) so maybe someone else will chime in.
I also backpacked the Mazatzal from both the west and the east sides. The east side is rather rugged with rocks on the trailhead I used; maybe a more local person has a better way in. The west side (banks of the Verde) is a much nicer trail, awesome freaking views, but the Bloody Basin road almost killed my 4x4 (there were remnants of about 5 vehicles, including one Maricopa sheriff's vehicle). Been trying to plan a return as my camera failed on that trip. Only problem I had on the west side was a duck hunter blasting away, even scaring other duck hunters.
My other hike in that area was Aqua Fria just off I-17. Mostly boulder-hopping but a unique area. Not much of a trail though, and your vehicle is parked right off the freeway. There's other areas south of Phoenix that I haven't explored.
Needs no intro but might be out of your stated drive time (think it will take you 12 hours just to get to El Paso):
The 'sky island' effect may mean the higher mountains may have snow on them than the central mountains. In the southeastern Chiricuahuas (closest to me off I-10), I have gone through thigh-high snow drifts into April most years. The mountains of Flagstaff have a XC area and will likely be snowy. My girlfriend and I barely dodged ice in the backcountry of Sedona during one Easter hike. Travel-wise, last Dec, I spent an unplanned night in Tucson when a cold front put some hazardous ice near Benson AZ and Lordsburg NM.
Driving and Cities:
Not that I minded being 'stranded' in the southwestern cities of Phoenix, Tucson, or El Paso. Seems the bad part of these towns are right below the I-10 freeway in the central cities but the rest is Ok. A good room in El Paso and Las Cruces will be pretty pricey btw if that's a concern, due to a boom in cross-border production/construction (deng business travelers); there's really nowhere to camp unless you get off the highway, past Deming or around Columbus (Pancho Villa St. Park). Southwestern cities in the NM/far west TX borderlands really want you to experience their hotels !!!. Also El Paso, Phoenix, and even Tucson have rush hour traffic. Not as big as DFW but still big enuf.
Speaking of New Mexico, it's a bit higher in elevation than most of Arizona, and will be colder. I've backpacked the Gila in December and once got caught in a cold-snap that went into the single digits. Brrrr. I may go back with more snivel gear but nothing like seeing a hot springs smoke while surrounded by ice. Hope this helps.
(ed: putting closer locations on towards the top)