There are local shows, some good, some a little sketchy. The A shows are at the KHP about an hour away and it is an easy 4 hours to Nashville and the excellent Brownland shows in a very nice, upscale area. You may find the KHJA website helpful-there are alot of links.
A level trainer wise, I know and like Leslie Governo and she also does some local showing. Rick Francher is based there too, or was-haven't seen him lately. But he is a real heavy duty A show trainer/rider and on the road a great deal of the year and doubt he has any school horses if you are not bringing one or planning to buy/lease.
So, depends on what you want and need. It's a good area, affordable-especially coming from San Diego. Climate is not bad and most things are close for somebody from out west.
When opportunity knocks it's wearing overalls and looks like work.
My farm is about 40 minutes outside of Louisville and we do some limited boarding and try to insure we have a good cohesive group. I love my farm and the area, and have met some great people.
I do the A shows at KHP, and sometimes Brownland, and usually for local shows go to Lakeside Arena in Frankfort, where they usually have monthly indoor shows from x-rails to 3'6" jumpers and 3' hunters. It's a nice place for newer riders, and for green horses to get in the ring without spending $1K for a weekend.
There are a few trainers in Lexington, not as many in Louisville that I know of. I have had one from Lexington out to the farm for lessons and am trying to get someone on a regular basis.
Feel free to PM or email if you'd like any more info on the area or want to come visit the farm sometime, even just to meet more horse people. Good luck! I LOVE KY!
Destiny is not a matter of chance, it is a matter of choice; it is not a thing to be waited for, it is a thing to be achieved. - William Jennings Bryan