In Nashville do all the stuff Nimrod said.
In Memphis take all your stuff into the hotel room with you, bar the door, and don't come out until daylight.
Just kidding.....sort of..
I work out of Memphis but live 250 miles away in central Mississippi. Memphis really isn't a very nice city, it's pretty much a dump. There's good BBQ, the Rendezvous is as good as any. Beale street has been cleaned up a lot over the last few years, plenty of bars and decent music. It's definitely tourist geared though. Don't get far off of Beale street, there are some real rough neighborhoods right around the corner. The Memphis Redbirds have a really nice park downtown but I think you're a couple of days early for their season opener. Graceland is a few miles south out near the airport. The neighborhood around it is real bad, finish up and get out of there before dark if you go. Graceland is worth a visit if you're a fan of the King, you've gotta see it once. The Peabody hotel is right downtown and you can go see the ducks walk. I know it's very touristy, but the ducks are just cool.
Midtown is the nicer area of Memphis, it's where the old money is. Plenty of good restaurants and nicer bars and music scene. Most of the museums are there as well as the zoo and some older mansions are opened for touring. It's too far to walk from downtown, and you wouldn't want to walk through most of the neighborhoods to get there, you'll need to take a car. Midtown is where I'd want to concentrate my efforts if I didn't want the real touristy stuff (and didn't want to get mugged).
I pretty much draw a 75 mile circle around Memphis and don't go into that unless I'm going to work. Oxford, MS, is about as close on the south side as I want to get, and Shiloh Battlefield (highly recommended) is about as close as I want on the east.
