Just outside of Mesa lies the large hilly desert-like area of Tonto National Forest. There were some amazing views at different points along the way. The drive is really beautiful, though some of the drop offs along the side weren't for the faint of heart! We didn't do much hiking but I imagine there are a lot of great places throughout the forest getting out and exploring on foot! If you want to get out into some scenic, wild places near Mesa, Tonto National Forest is a great stop for you!
My favorite place that we visited near Mesa was Tonto National Monument, which is a little less than a two hour (beautiful) drive from Mesa. The Salado Native Americans lived in the area between about 1150 A.D. and 1450 A.D., and they left some really fascinating cliff dwellings behind them. We visited the lower cliff dwellings, and the hike up to them (and view from them) were absolutely beautiful. We met a very nice park ranger, and she went with us to the top and gave us a little more information about the place. Combining beautiful views of the desert, hiking in excellent weather, history, and culture, this was definitely a great stop in Arizona!
Goldfield Ghost Town is an Old West mining town converted into the best tourist trap on the Apache Trail. There we met an entertaining fiddling prospector named 'Garbanzo' with a wife named 'Chickpea,' panned for gold (and found a bunch of garnets too!), visited Arizona's largest live display of venomous reptiles and invertebrates, and purchased some handmade pottery as souvenirs for our loved ones back home.
The Mesa Southwest Museum (now the Arizona Museum of Natural History) was a very nice natural history museum, filled with Native American pottery, dinosaur bones, Old West artifacts like a replica jail, a stagecoach, and a place for panning for gold, and other unique artifacts like a suit of conquistador armor. The dinosaurs are one of the most impressive parts--there's a hall of dinosaur bones and even a Dinosaur Mountain, where you can see and hear dinosaurs!
A unique place in Mesa is Organ Stop Pizza. My sister and I were hesitant to go, as it was a favorite of the retirees who winter in Mesa, but it was actually very entertaining. The pizza was excellent and the pipe organ more impressive than expected. The organ player knew dozens of songs, and took requests. My personal favorite was when he played Under the Sea and bubbles as well as music filled the room!
Tortilla Flat is an "authentic old stagecoach stop," where we tried prickly pear ice cream, explored the gift shop with typically Southwestern souvenirs--scorpions in crystal, pottery, turquoise jewelry, etc., and decorated a dollar bill to add to the hundreds from other tourists lining the walls of the restaurant there. It's touristy, but it's in a location with some really great views of the desert, and what I think is called Canyon Lake (see above).
If you're at all interested in engineering, this stop could be of special interest to you! There's the Roosevelt Dam (above) which is huge, and then there's also a really modern bridge on the "high side" of the dam (I couldn't find a good picture, but it's pretty cool). At the time of completion in 1911, the Theodore Roosevelt Dam was the world's largest masonry dam. This location is also really close to Tonto National Monument, and the drive to it from Mesa is really pretty!
If you're in the Mesa (or even Phoenix) area, you should consider a few of these seven destinations to check out some fun areas for your trip! Tortilla Flats and Goldfield Ghost Town are more touristy, but we had a lot of the other attractions almost completely to ourselves, which was really a treat!