I do not believe there overnight camping at Nunn's park there many campsites very close within 20 miles in almost every direction rough camping is a little further away maybe 30 miles but there are KOA Campgrounds and Mountain Valley RV Resort right at the top of the canyon in Heber Utah
Nunns Park is open from mid April to early October. The northeast portion of the park, the lush green grassy areas, are day use only and provide picnic tables, barbeque stands, and fire pits, and horseshoe pits, all free to the public. To the southwest is the camping area, they do not reserve campsites, first come is the rule. The camping area is a fee area, whether overnight camping or just picnicking, as of 2019 season its $20/day. They have two pavilions available for group activities, these can be reserved by contacting Utah County Parks at 1-801-851-8640. They can be rented from the Camp Host if not already reserved.
There is a campground, it costs 25.00 dollars a night to camp. I'm not sure when it opens though.
There is a camp ground at nuns park. I think it opens in May and closes in September. It is located to the left of the stop sign. You have to go under the overpass.
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