Chris, I know the general feeling is that Arkansas is a backwater state, and it is of sorts but believe me there is all kinds of stuff to do and see, especially if you are an outdoors person.
On the model side there are 3 hobby shops in the Little Rock area. (note: I refer to selection of plastics I mean cars, armor, aircraft ect... pretty much everything)
The Hobby Town USA in Little Rock itself is very nice and they have a good selection of plastics. A friend of mine works in there and his sole job is taking care of the plastics and associated stuff. They have some aftermarket items (live resin, legend stowage and some others)They carry a decent amount of books and several paint lines as well (life color and Vallejo Air. Incidently, Hobby Town is where the local IPMS chapter meets, of which i'm the President.
Rail and Sprue hobbies is in Jacksonville a few miles north east of Little Rock. They have a huge selection of train items but the plastics is pretty good to. They have a few AM parts. They do have a great area for scratchbuilding supplies and tools. His paint and finishing product area is fantastic. Rail and Sprue carries many paint lines including Tamiya, Alclad, MIG, AK Interactive, Vallejo and oodles of others. This is where I go to get most of my paint supplies.
A couple of miles south west of Little Rock is another shop called One Track Mind. Again, they handle mostly train items but the last time I was in there they had a good selection of plastics and they were generally cheaper than the other two shops. They also have a good bit of scratchbuilding stuff but less paint than the other two.
As far as Museums: Here is a list from wikihttp://en.wikipedia.org/wiki/List_of_museums_in_Arkansas
There is a military museum in Jacksonville and the USS Razorback WWII submarine tied up in the Arkansas river in Little Rock. There are some others in the North West part of the sate as well.
As far as cultural crap goes...
The River Market in Little Rock has some cool places to eat. There are a TON of little hole in the wall joints to eat, too many to mention. If you like BBQ though hit up any of the Whole Hog restaurants. If you're up for a little drive Hot Springs has a lot of touristy stuff, shops, Bath House Row (pretty cool actually) It's about an hour drive south west of Little Rock. There is a horse track in Hot Springs as well that runs live racing from about Jan-Mar and simulcasting most of the other time.
If you're here for few days and want to do some outdoors stuff there are many many many hiking trails around. Pinnacle mountain which is just on the edge of Little Rock. Down toward the Hot Springs area there are 4 major lakes to enjoy with all the camping opportunity you can stand.
Arkansas has 4 distinct geographical areas (mountains in the north, prairie on the west, river delta in the east and swamp in the south. All 4 are very very hot in the summer. It's not uncommon to hit well over 100 degrees coupled with 75-90% humidity when there has been rain. Last year we had about a week at @ 115 degree heat index.
I could really go on all day but this just gives you a hint. There is a lot to do here... Difference is there generally isn't a huge flashing sign over it.
Hit me back if you have any more questions.