Deliverance wasnt set anywhere near Arkansas.
Let me take a stab at it.
Luiz, you will actually be within a hour or less of where I was born and raised in Newport, AR. Unfortunately for you, you will be in the extreme NE part of the state, right on the border with both Missouri and Tennesee, and part of the agri belt.
Closest town of any real size is going to be Jonesboro, AR (where I enlisted into the Army as a matter of fact), but I cant really speak to whats available there now since the city has more than doubled in size since I was there last. Its a college town, hosting Arkansas State University, and has a population around 70k or so.
Your best bet for interesting things is in Memphis proper. You can always take the tour of Elvis's place, which is nice. Memphis also has a nice zoo. Night life centers around a lot of established night clubs/restaurants around the Beale Street area. Good food would include fried catfish, barbecue of all types, and a pretty good selection of sea food oddly enough for a town far away from the coast. My dad used to take me every year on my birthday to a seafood place there called Pappy and Jimmys and we would pick a live lobster out of the tank for dinner. Hehe, place is closed now, but many of its type are around Memphis.
One thing I can absolutely recommend is spending some time at Mud Island at Memphis. Mud Island is something the city built onto what was once a large sandbar on the Mississippi river. They turned it into a river museum, concert venue, etc. etc. If you ever saw John Grishams 'The Firm' it was featured a lot in the film. One of the most amazing things there is a scale replica of the entire Mississippi river with flowing water that runs the length of the Island (rougly a mile or so in length). If you might be interested in the culture that arose from all around the river, you may find it very insightful and fun.
If racing betting is your thing, they used to have a greyhound dograce track across the river in West Memphis Arkansas. Went there a couple of times, but I found it to be not as fun as the Horse Racing track on the other side of the state.
Hope that helps.