I'd skip the car. Beale street is a block away (think Disney version of Bourbon Street), and there's a shuttle bus from there to Graceland. You can also arrange a "package" Graceland tour from the concierge which includes a quickie tour of the downtown (i.e. a "drive-by" of Sun Studios and the car lot where Elvis bought his Caddies).

BTW, the Peabody is gorgeous in the public areas, but I found the rooms rather shabby. They also gouge you on the parking, so one more reason not to rent a car.