Nacogdoches is blessed to have many wonderful parks. It's highly recommended to visit them all during your stay here. The Liberty Hall near downtown is also the start of a great trail system throughout the city, also recommended.
The best park for little kids is Maroney Park, near the high school.
Best park to visit during daytime only, not at night, is Pioneer Park, near Unity Church, on South Street. Fabulous park, huge, many acres of land, really nice.
Best park for flying kites is Festival Park, near downtown, big open field.