Just six miles southwest of town is Benbrook Lake (817/292-2400, www.recreation.gov [1]), where the U.S. Army Corps of Engineers administers six public campgrounds offering sites for utility hookups and primitive camping.
Another option east of downtown is Sunset RV Park (5017 White Settlement Rd., 817/738-0567) in the village of Sunset, a rural area surrounded by ranches, farms, and other small towns. The park offers full hookups, free wireless Internet access, showers, and a laundry room.
Links:
[1] http://www.recreation.gov