If you can, do karshner caverns down there, tombstone is cool if your into the old west stuff, the air and space museum is pretty cool. Went there as a kid about 15-17 years ago. Probably got cooler things now.
If you drive up to Sedona, you can hop on a pink jeep tour. You will want to make sure it takes you on broken arrow. Hardest trail there that will give ya some thrills in those top heavy rigs. Super pretty area up there too as you drive in and awesome shopping/dining up there too. Then you can head up 89a through oak creak canyon and come into flagstaff if you want. All 2 lane through the canyon which is really nice. You will take the i17 to camp verde. Just out side of camp verde is highway 179 which will take you to Sedona.
West of phx, there ain't shit. Either go north, south or east.
From mesa, if you take the 60 all the way to superior, miami, and globe, then follow it north to show low, you will again hit some beautiful scenery and a really cool water fall to stop and look at. Globe and superior are old mining towns too so you can split off and find some old ones if you wanted. Its about a 4 hour drive to show low that way. Then you can either take the 260 around to heber/Payson or head back the way you came. You will hit the mogillon rim if you take the 260 back and again, breath taking veiws.
Btw, the food joints I suggest are more on the west side of where you are. Might be a drive just for some food. Out east there, I don't know a ton of places. If you head into desert ridge shopping area off Tatum and the 101, there is good food there to pick from. When you get into mesa, I'm kinda out of my realm there.
How long you guys here for?