Second the recommendation for Red River Gorge.  It is really easy for dispersed camping- you just have to stop in at the gas station right off the mountain parkway to grab a permit to hang in your car.  Its been getting pretty crowded on the weekends though, so weekdays might be better if you are looking for any solitude.  You might also try to get one of the Outragis map sets that show the unofficial trails (we always pair with Alltrails so we can see where we actually are on the map as we go, as it can be easy to get turned around).