Tonto natural bridge is off of 87/260 about 12 miles out of town. Cost is $7 per person and you should see if it is open before heading out.
The airport is a fun place to have breakfast at a picnic table and watch the helicopters and small planes land. Then if you head West you can drive on Earnheart way and see homes that have plane hangers attached. This is fun to see the planes up close. The restaurant at the airport has GREAT pie..
If you are up for a drive there are many lakes within 35 to 50 minutes from the Payson house. The lakes are East of Payson off of the 260. Google which one you want to go to. Woods Canyon Lake rents small boats. Willow Springs i s clean and fun to catch crawdads. Woods Canyon Lake; Willow Springs Lake; Black Canyon The Rim i s a great place to hike and walk on a paved road to see the beauty of the mountains if that is your destination.