If you want to really see Arizona, you will unfortunately have to rent a car. Our state's public transportation will only get you between cities and not stop to see the true beauty of the wilderness between them.
Desolation? Not a whole lot around Phoenix. And reaching the desolation just outside of Phoenix usually requires a few miles down unpredictable dirt roads. You could head south to the Tohono O'odham Nation and will certainly find emptiness. There's a little back road that runs between Stanfield (west of Casa Grande) and Santa Rosa (west of Sells) that is one of my favorites, but it's all paved. However, besides Kitt Peak, there's little else to do there.
From Phoenix, there's also a side trip you can take west to around Buckeye and head north on a small, paved road to Wickenburg. It's extremely desolate and a very interesting drive.
The famous red rocks are in Sedona and Oak Creek Canyon, which is about an hour and a half drive north from Phoenix. That's actually a must for any AZ trip.
Although I'm biased, I would also strongly suggest that you head south to Tucson for some gorgeous, unspoiled desert. Lots to do in town as well.

You definitely have to rent a car, unforutnately. Sedona is absolutely beautiful but it's quite a drive and is best if you take at least a half day to see it. If you're only here for two days it might not be worth it.

If you're into hiking or seeing beautiful desert close to Phoenix, I would suggest The Superstition Mountains. The range is located in the Lost Dutchman State Park and is just east of Phoenix, about a 45 minute drive from the center of the city. You take the 60 freeway and get off at Idaho Rd. It's $3 or so to enter. www.pr.state.az.us/Parks/pa...hman.html

There is a discovery trail around the base of the mountain if you don't want to hike. This trail has various placards along it describing vegetation and animals in the area. It has beautiful views of the mountain.

There are a handful of trails that go up the mountain. You can get a map when you enter that tells you which ones are rated easy to somewhat difficult. All of the trails I've been on have some of the most amazing views of the entire Phoenix metro area, especially considering the ease of the trails. The views of the vegetation and mountain don't really compare.

There is also Camelback Mountain right in the center of the city, with absolutely stunning views, but that hike is hard even for someone in excellent shape. I've done it twice- wouldn't recommend it.

Thanks for the advice much appreciated.- Looking forward to exploring these options.

I just arrived in phoenix, my bag didn't... arg!

I agree with the above posts.check out the Superstitions....the view of Fish Creek Canyon is worth the drive alone.if you prefer hiking over driving you can park your car after you cross the bridge over Fish Creek & hike up the canyon a ways.to really experience a desert oasis hike back a little over 1/2 mile.i did a wonderful trip a few years back hiking down Fish Creek from the headwaters below Reavis Ranch trail down to the Frog tanks & then down the Canyon to highway 88.