From Memphis International Airport around 20 minutes south of Downtown, the best way of getting into the city is to hire a car and drive, and most of the major rental companies have offices at the airport. If you're coming to the city in homage to Elvis Presley, the city's favourite son, then book well in advance, and you can still get hold of a big pink Cadillac just like the king's so you can get around in style.
They don't like drink drivers in Memphis, so if you're going out at night and indulging, then use a cab to get back to your hotel, or go to jail.