Depends what area you're looking at as to what's close-by, as well as which side you want to play for (Confederate or Union) and which arm (infantry, artillery, cavalry, or other).
The 1st Arkansas Infantry is a good group, centered around the Pine Bluff and south-central Arkansas area. They have web site, mentioned elsewhere in this thread.
2nd Arkansas Mounted Rifles are located in the Dardanelle/Russellville area. They're an infantry outfit, dispite the title.
There are two groups in southwestern Arkansas repesenting companies D and E of the 3rd Arkansas Infantry, with a little overlap into SE Oklahoma and northern Texas.
The 6th Arkansas is located mostly in the Little Rock area. See http://www.geocities.com/capitalguards.
The 7th Arkansas is located primarily in the northeastern corner of the state.
The 9th Arkansas is in the Hot Springs/Arkadelphia area.
The 10th Arkansas has a small group in Conway.
The 15th Arkansas is located up in the Fort Smith and eastern Oklahoma area.
All the above groups are primarily Confederate units, though they occasionally "galvanize" to Federal to try and keep the force ratios a little closer to reasonable at events.
The only full-time Union organization is the 37th Illinois, out of Little Rock, though there are a couple of other Union groups across the river in Memphis.
The best recommendation is to shop around and see which group is most convenient and best fits your needs...