I lived there for five years before moving to Memphis, and have stayed in the Alluvian a few times. It's a fantastic hotel, and the spa is world class (literally - it was ranked #13 in the world by a prominent women's magazine, although I forget which).
Greenwood is a nice place to visit. If you are there on a Friday, call Viking Range Corporation's HQ (662-455-1200) and see if you can schedule a plant tour. The Range plant is an awesome facility. Also, make the trip out Money Road and visit Miller's Grocery, where the
Emmett Till story sadly got its start and the Civil Rights movement was essentially born. You'll pass the likely burial place of
Robert Johnson on the way there.You can visit both in an hour.
As far as food goes, Giardina's at the Alluvian Hotel has one of the best filets I've ever eaten. Lusco's also has a great steak, and you can brown bag wine or liquor. For lunch, go to the Crystal Grill. Absolutely everything on the menu is fantastic, but the broiled KC pork chop, the blackened catfish, and the fried spring chicken are my favorites.
For such a small town, Greenwood is steeped in history, and there is actually a lot to do. And I would say that on a per capita basis, there are more great restaurants there (and throughout the Delta) than anywhere in the country.