Load up your car with your bike and take it to downtown Memphis in the summertime. There are long, windy bike paths and roads that follow the Mississippi river downtown. Also, check out Shelby Farms. This is a large, expansive park in the middle of the city that has grazing buffalo, lakes for sailing, and tons of trails for walking/jogging/biking.
If you want a larger lake, many people in Memphis drive to either Horsehoe lake in Arkansas, Pickwick lake in west Tennessee, or Sardis Lake in Mississippi. All are roughly an hour-hour 1/2 away and offer great things to do in the way of leisure. I have really fond memories as a kid swimming and fishing in these lakes with friends and family.
If you are interested in something closer, the community of Lakeland, TN is fairly close to town and has plenty of real estate surrounding a decent sized lake.
Lastly, if you are into kayaking or canoeing, the Wolf River runs through the city, beginning in Moscow, TN and ending at the Mississippi River. I've gone kayaking and canoeing on the Wolf River and find that the best time is in the fall when you have colorful forests hanging over the river. Plus, you won't see many water moccasins then either!