Mitchell Lake has a nice little campground we stayed at before... we were towing the trailer behind our little MOHO and they gave us a pull through... I believe it is either City owned or county... not expensive... nice sized spots. folks running it when we were there couple years ago were really nice.
Depending on which route you take, Hillsdale State park has a nice campground east of Ottawa, KS on hiway 68... Might be a good overnight option. Sorry I don't know the campgrounds west of I 35 well enough to give you good options there.
Martha (AKA RVM45), Bob, and Bess the Border collie
22'Honey Sportscruiser on a 1988 Ford Econoline.
Sometimes towing a powered Parachute.