You can pitch your tent or park your RV just 15 minutes’ drive from downtown Memphis [1] at T. O. Fuller State Park [2] (1500 Mitchell Rd., 901/543-7581). The park has 45 tent and RV sites, each with a picnic table, fire ring, grill, lantern hanger, and electrical and water hook-ups. Sites are allocated on a first-come, first-served basis; reservations are not accepted. Rates are $18.50 a night per site.
On the north side of Memphis [1], Meeman-Shelby Forest State Park (910 Riddick Rd., Millington, 901/876-5215) is a half-hour drive from downtown. Stay in one of six lakeside cabins, which you can reserve up to one year in advance. The two-bedroom cabins can sleep up to six people. Rates are between $50 and $80 per night, depending on the season and day of the week. There are also 49 tent/RV sites, each with electrical and water hook-ups, picnic tables, grills, and fire rings. The bathhouse has hot showers. Campsite rates are $14.50–17.50 per night.
Links:
[1] http://www.moon.com/destinations/tennessee/memphis
[2] http://www.moon.com/destinations/tennessee/memphis/sports-and-recreation/parks/t-o-fuller-state-park