The Quapaw Quarter has a pretty active preservation organization, the Quapaw Quarter Association, that has helped to drive and support preservation efforts in the QQ and in MacArthur Park as well. Their website is www.quapaw.com.
The Central High area is just to the west of Quapaw and also has some great houses, though it doesn't have the reinvestment in it at this point that Quapaw does. Still some great houses there too.
If you are interested in preserving historic neighborhoods in LR/NLR and around the state or just interested in historic preservation in general, you should check out the Historic Preservation Alliance of Arkansas (www.preservearkansas.org).