Tonto Natural Bridge State Park is surrounded by several lovely little towns with some fun options for where you can stay.
Our first suggestion would be to use AirBnB or similar sites to find a space to rent in the towns of Payson, Pine, or Strawberry. This is how we usually lodge when we have trips to the area.
If you are not comfortable with the first option, we have found a few motels in the area you could use:
Our venue is about a 2 hour drive from our home in Chandler. The road into the park is narrow and windy, but paved and painted. We would suggest bringing your own transportation or organizing rides with other guests.