Wow, that's a ton of driving for you all the way out there. I'm in west Mesa. I go to Sycamore Creek or Sugarloaf Mtn. when I shoot. Here's a map:
Click here for Google Maps
Hope that link helps you. From where you are, you can probably take Power Rd. North until you get past Saguaro Lake. Go over the overpass to Highway 87, and you'll hit dirt road. That takes you right there.
One word of advice though is to check on the Tonto Forest's website, to make sure there isn't a fire restriction at the time.
Hope that helps!