Yes
The property at 339 Conference Center Drive (with the main office, lake loop, Piedmont loop, and wetlands boardwalk trail) is open to the public from 8am-5pm every day except Christmas Day. The Iron Ore Belt Access at 6068 North Church Street is open at 8am every day, and closes seasonally based on the following hours: November to February: 8:00am to 6:00pm March to May, and September to October: 8:00am to 8:00pm June to August: 8:00am to 9:00pm Source: "Park Hours" https://www.ncparks.gov/haw-river-state-park/home
Yes, they have a gaga ball pit and really beautiful hiking trails. One of the trails leads to a natural area which is a bog garden with bridges over it. Very beautiful!
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