There is really nothing near the Ark, unfortunately it is 30 minutes away from anything else interesting. The casino I assume is Belterra. It is decent. They have/had a good buffet with all you can eat crab legs, price was just over $30 a person last time I went there. The roads once you leave I-75 are very narrow and curvy adding a lot of travel time.
No distilleries near the Ark but you do you have Elk Creek Vineyards if you drink wine. They have a very nice building. The property also features a hunt club with sporting clays and lodging.
https://www.elkcreekvineyards.com/http://www.elkcreekhuntclub.com/https://www.elkcreekvineyards.com/page-350851/Lodging.htmlIn that area is also the Kentucky Motor Speedway.
https://www.kentuckyspeedway.com/There is a distillery near the speed way. I know nothing about them but they do offer tours.
https://www.neeleyfamilydistillery.com/For big name distilleries Frankfort or Versailles would be the closest and over an hour away from the Ark. Lexington has a lot to see including breweries, wineries, and some distilleries. That would be an hour from the Ark as well.
The Ark itself is a lot of walking and almost nowhere to sit to take a break and I think just one small snack shop part way through. They have food outside the ark but once you go in it is several hours of looking and walking to see it all.
For firearm laws Kentucky is now constitutional carry and it applies to non-residents inside the state border. If you can legally own a firearm then you can legally carry concealed in Kentucky without a CCW. Not sure on the Indiana laws any more.