Potato Creek State Park is a state park in Indiana with mountain bike, hiking, and horse trails. There is also a beach for swimming, an electric campground, cabins, and a horseman-specific campground.
Park information is available here: https://www.in.gov/dnr/parklake/2972.htm There are multiple parking areas that have access to trails, but the best spots are the Nature Center or cemetery parking lots.
Open year-round. During the summer weekday visits are best, as the park can be crowded on weekends. Avoid on Fridays preceding holiday weekends, as the line to enter will be very long.
There is an entrance fee daily during the peak season and on weekends during the winter.
Dogs are allowed, but must be kept on a 6 foot leash at all times. There is also a dog beach that is open seasonally (May thru September).