Last week, we went to Prairie Grove Battlefield State Park to take advantage of the free apple picking we learned about on our previous visit. I called ahead to see if it was that time of year yet and was surprised to learn that late-August was almost too late for picking! When we got there, Buddy handled the apples on the ground, while I climbed some trees to reach more attractive specimens. Angela developed an effective modified pinata approach using a stick and tennis racket that yielded some excellent, only slightly bruised apples.
I didn't get verification, but it seems like apple picking season is roughly the month of August. To the non-professional eye, there appeared to be two varieties of apples. Both were delicious, but the smaller, brownish, less attractive ones were incredible.
The park has a 1-mile paved trail, pavilions for events, historic houses, and battle reenactments in early December of even years.
Update 7/24/2014: I went back at the end of July this year and it looks like the first half of August will be a great time to go pick. I got some good ones on this trip, but could tell many weren't quite ready.