I have been known to drive a few of the blokes on this site around the distilleries.....but seriously there are 3 parts, local, Bardstown area and Frankfort. Best on the Frankfort side are Buffalo Trace, Woodford and the new Castle&Key (Used to be the Old Taylor site) distilleries....Four Roses too if you can make it but lately the experience has been meh. Lexington is trying but not yet worth the trip yet IMHO
Bardstown, Beam is crowded but lots of tasting opportunities, Maker's is a good experience and Heaven Hill is somewhat of a sanitized experience. Make sure you hit up Willet, they are more intimate. Hit up the cooperage toward Lawrenceburg although tours are limited. Hit up Kurtz, Mammy's or Old Talbott for lunch/dinner.
Locally, a lot of recent options have opened including Evan Williams, head over to Bulleit too, while not a huge fan of the bourbon the experience is good. Restaurants can be found with a plethora of offerings. Downtown, hit up Down 1 bar, Dish on Main is an off the path dive where you can get a bourbon and a burger cheap. the Silver Dollar is nice. Feast Barbecue has bourbon slushies which are fun and good food, people line up there.
Other distilleries of mention are Peerless and Copper and Kings (Brandy and Absinthe) Angels Envy is open but I am not a fan.
Mint Julep tours is the equivalent to the limos in wine country. In most cases though it is really difficult to drink enough to get drunk, but if on the safe side then go for it.
Uber/Lyft isn't really an option as there are significant distances between the sites.