There are a quite a few places in South Tampa to enjoy a public pool for a small entry fee. The City of Tampa has several pools located around South Tampa that offer amenities for children and adults; Bobby Hicks, Interbay , Roy Jenkins, and the Spicola Family Pools. The South Tampa YMCA has a nice pool complex.
Also, if you are interested in having a drink while sitting at a pool you may wish to check out the Hotels in the area. Many of the larger hotels have poolside bars and will allow the public to use the pool for a fee. Check out the Tampa Marriott, Tahitian Inn, Hula Bay or the Epicurean.