I haven't flow in to Ashland, but did visit the museum a couple years ago on a two-lane road adventure. We're in the habit of stopping in on small town museums every chance we get. Some are good, some forgettable.
The museum is primarily a pretty decent County museum, some good photos from the late 19th/early 20th century. Although the well-to-do are well documented, as is typical, theres some decent accounts of the ranch and farm life and people of the time.
There's a wing of the museum dedicated to local hero, Hal Krier, including his unique biplane (which I had the privilege so see perform in a land far ago and long, long away). Quite a bit of aviation memorabilia.
The aerodrome is only a mile or so south of town. Don't know if there's a courtesy car (typically there is in that region), but wouldn't be a bad walk to town.
If you're in the area, should also see the Mid-America Air Museum in Liberal, which has lots of military stuff, including decent examples of Piper, Aeronca, Taylorcraft, and Stinson WWII Liason aircraft, for comparison. Quite a few experimentals, and some jets through Vietnam era. It's right on the aerodrome, and has expanded quite a bit since I used to fly in there on business.
Thanks. cubscout