Look at these four; Jamestown, State Dock, Conley Bottom, and Lee's Ford. The rest are two small or secluded to pass on these four. Some will argue for Burnside, not a fan. I worked on Conley Bottom when I was in high school and college during the summers and can attest that there will be no marina that will see to it your boat is more secure and taken care of when you're not on it. Now, it's not a big party marina. If you're looking for a place to park in the slip and raise hell wandering the dock before crashing in your boat, not the spot. Jamestown is a little more lax there but it's in Russell County, an extra 30 min away from my suggestion. State Dock is the biggest but its run by the state and it's not going to wow you.
I don't know you personally but you're a Lee's Ford man. It has easy access off of 80 in Somerset so coming from Lexington it's probably the easiest to get too, it's one if not the only marina that allows alcohol sales, the restaurant on site is more than serviceable , and the clientele is very much looking to be seen as much as get out and boat. My advice, if you have a boat you can sleep on go moor for a night and see. It's the perfect time of year to get a feel.