Mariner's Museum Park
Around the Mariner's Museum is a 550 acre park, with a running trail, a lake, picnic areas, and benches. The park is open to the public daily and is free. I understand that there is another Newport News park which is not free.
I have not used the park, as I concentrated on the museum, but the website says:
"The famous Lion’s Bridge, a dam that provides a breathtaking view of the James River, remains a highlight for visitors – a perfect family gathering place to enjoy the Museum Park. The beauty of the dam is enhanced by several fine pieces of statuary designed by Anna Hyatt Huntington, sculptor and wife of Museum founder Archer Milton Huntington. Four stone lions were mounted on the ends of the parapets of the dam in October 1932. Anna also created and dedicated a monument entitled Conquering the Wild that overlooks the Lion’s Bridge, the park, and Lake Maury."