The pioneer settlements at Boonesboro & Harrodsburg are neat if you're into the regions early history. I personally like the museum at Fort Harrod. The Blue Licks Battlefield State Park is the site of the last battle of the Revolution with a nice museum, but about 40 miles north. Daniel Boone's last Ky. residence is not far from there.
The Henry Clay museum, The Mary Todd Lincoln house.
Buds is a big place with a lot, a whole lot, of mostly modern or new guns. Two shooting ranges.
Classic Arms & Archery has a nice selection with some really nice older Smiths, Colts, Winchesters & the like available.
Evans Firearms has a large inventory.
Antique & Modern is/was the high end gun shop in town, but scaling back their hours. Check for schedule.
I mention the last 3 because they are very close in proximity to one another as far as small cities go.
Then there's the Ky. Horse Park and/or The Blue Grass Country driving tour for the ponies or just some pretty countryside. The pristinely manicured horse farms are a pretty sight.
I can't think of anything that really pops, but have been here for 63 years & maybe taking some of it for granted, Let me know if you'd like specific info on something.
D. Boon's place: