If you land at M01, I suggest stopping to eat at the Arcade (
http://arcaderestaurant.com/). Food is good (for a diner) and has some history, being the oldest restaurant in Memphis. I'm bleh on Beale St. Hard Rock just moved or is moving into a new place, so that'll be done up new. I like Graceland, although no one ever seems to agree with me on that. Word is the plane display is leaving by April next year. Sun Studios is downtown. You might see about scheduling some dual time in a Stearman at M01. There's a riverboat tour too, although I bet those are all up and down the river. Oh, and the Memphis zoo is pretty nice. It gets high marks. They even have a pair of Pandas. If you want good food, there's definitely a lot of choices if you get a car. Elegant Farmer (
http://www.theelegantfarmerrestaurant.com/) in mid-town is a great farm-to-table sort of place. My BBQ preference is the Germantown Commissary (
http://www.commissarybbq.com/).
I don't know how far you mind venturing from the Mississippi, but there's an aircraft disassembly facility at Tupelo airport. First Saturday of each month they do tours and it's cool. There's also a car museum and outlet malls in Tupelo.
Tunica is along the Mississippi and you might catch a show or buffet (or gamble, of course).
Again I don't know if this is too far off the river for you, but Walnut Ridge has a nice little museum on the field. It shows about the history from when it was WWII training base. They've got a restaurant too, with an old 737 you can eat in. Food isn't great, but I've never gotten sick off of it.
Up to Halls, TN and there's another little museum on field. It was also a WWII training base. I like this museum better than in Walnut Ridge, but the field itself isn't as nicely maintained. The concrete is getting rough.
At Dyersburg, just north of Halls, there's a restaurant on field that's only been there 9 months or a year. I've only been once for a Sunday brunch and enjoyed it. Chicken and Dumplings were excellent and they claim almost everything is done from scratch.
Going further north is Sikeston, MO. There's a Lambert's there (
http://www.throwedrolls.com) that'll pick you up from the airport.
Near there in Dexter, MO is another airport with a restaurant on field. I've enjoyed many breakfast there on Saturday mornings and it can get quite crowded.
North some more is Cape Girardeau. It has a restaurant on field. I think this is where Rush Limbaugh is from and they have a small display about him in the airport, which is weird.
Apparently my flying centers around food.
