To visit that National Preserve, I would camp at El Dorado State Park, El Dorado Lake, about 50 miles SW of Strong City. That's assuming I did not have relatives in Wichita or Emporia to stay with, and did not want to do it as a day trip from home.
I recommend El Dorado because I am more familiar with that park, than the parks and campgrounds on Melvern Lake, about 30 east of the preserve. Eisenhower State Park is on Melvern Lake, but I don't know the park.
I wont recommend Emporia RV Park only because of its location along the highway, but you might find that kind of noise OK for an overnight stop or short stay. I sometimes stop that close to the traffic when I have to, but really prefer to be in a campground on a lake or stream where there might be trees and shade.
You might consider 50 miles to be some distance, but here we are accustomed to a 50 - 80 mile drive, each way, to go to dinner at a particular restaurant or to have an evening at the theater. It is a wide open spaces perspective. It would be like driving to Utica for the day, but the roads in Kansas are good and traffic moves well.
Tom Test
Itasca Spirit 29B