Do they have towels at the park, or do we have to bring our own?

They do have towels for rental, and yes you can bring your own.

You can bring your own towels or rent them on-site

You can rent towels for $5 or bring your own for free. If you bring your own, you can rent a locker or just use your towels to "claim" a chair in the "beach" area.

They have towels you can rent. I believe it was $5 per towel but not positive. I brought my own and rented a locker.

You can rent towels there