Assuming you want the ocean side, Mississippi beaches are closest, all about 6 hours drive. Not too much further to hit other nice beaches on the Louisiana or Alabama coast. Web page all about visiting this coastline.
Visiting Mississippi beaches specifically.
Memphis to Biloxi beach in MS: About 6 hours / 400 miles.
Memphis to Gulfport, Waveland, all about the same distance. Following Hurricane Katrina tourism is probably down in the area, so you might be able to just drive down and find somewhere nice to stay without booking ahead.
The area called the Emerald coast stretches from the Panhandle area of Florida in to Alabama.
Vacation rental on the Alabama stretch of the Emerald coast.
Some lakes a lot closer to Memphis have decent beaches, but whether you could go swimming I'm not sure. Try Lower Lake Beach MS.
Visiting Mississippi beaches specifically.
Memphis to Biloxi beach in MS: About 6 hours / 400 miles.
Memphis to Gulfport, Waveland, all about the same distance. Following Hurricane Katrina tourism is probably down in the area, so you might be able to just drive down and find somewhere nice to stay without booking ahead.
The area called the Emerald coast stretches from the Panhandle area of Florida in to Alabama.
Vacation rental on the Alabama stretch of the Emerald coast.
Some lakes a lot closer to Memphis have decent beaches, but whether you could go swimming I'm not sure. Try Lower Lake Beach MS.