We do not allow overnight camping at South Fork Park. For an evening Pavilion Reservation (3:30PM - 9:30PM) the cost starts at about $65 (Depending on the Pavilion and other Special Conditions). For updated costs and rental availability please visit; https://www.provo.org/Home/Components/FacilityDirectory/FacilityDirectory/45/200 -Craig C.
Unless you're planning on renting the Pavilion there visiting the park is free as far picnicking but you cannot do any overnight camping.
To my knowledge, South Fork Park closes at dusk and is not open to over-night camping. During the day of course it's entirely free. Vivian Park on the other hand (which you have to go through to get to South Fork) is another question entirely, for which I do not have an answer.
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