Hi Spiro,
It has been about 15 years since I stayed at Mammoth Cave Hotel, so I can't comment on the food there, but there is a Sahara Steak House in nearby Cave City that is decent. There really is not a lot around this area, so I would suggest you try out the hotel dining first and see how it goes. If not so good, then opt for the Sahara the second night.

As for Abraham Lincoln's birthplace, there really is not a lot to see there, and if the cabin itself is closed, I don't think it would be worth the time. I personally, would opt for a little time in Nashville. The Ryman Auditorium in downtown is a little piece of history. It's a shame you have to miss the Nash Trash Tour. It is a really fun time.

I think you will love the lantern tour of the cave, and the wild cave tour sounds like a blast.

Have fun and enjoy your trip.

Thanks Byllb

Looking further at Nashville, The Hermitage looks good. I wonder if anyone have any comment on Ryman or Grand Ole Opry Tours?

Spending time in Nashville would be a good option. Will second taking the self-guided tour of the Ryman Auditorium. The Country Music Hall of Fame is very good, as can be the Frist Art Museum (depending on what its temporary exhibit is, as there is no permanent collection here) or just strolling along Broadway to look into the bars and shops. All are close by the Ryman. According to Mapquest, Mammoth Cave is just under 100 miles from Nashville, so the amount of time you have to spend in Nashville will be a little limited.

If what I remember reading is true, the log cabin at Lincoln's birthplace is a replica, which may or may not matter depending on your interest.

To answer more questions:

--the Hermitage is well worth a visit, but you won't likely have time to see it and Nashville's downtown attractions in the partial day you have. You'll probably have to choose here, as they're a good distance from each other. Am assuming you have a car, as it's only accessible via car or Gray Line tour.

--I was underwhelmed by the current Grand Ole Opry complex and surrounding area. Nearby attractions such as Cooter's Place and Willie Nelson and Friends are tourist traps heavy on souvenirs, really worth it only for die-hard Dukes of Hazzard or Nelson junkies. If you've seen the Country Music Hall of Fame, the Opry Museum is pretty much more of the same. Opry Mills is just a huge mall. Probably the most interesting thing to see out this way is the Opryland Resort, but it's basically a series of interconnected large hotels linked by huge indoor gardens -- it's all very Las Vegas seeming to me. Nothing really floated my proverbial boat out this way, but others may feel differently.

Just South of Mammoth Cave is Bowling Green where we stayed a couple of years ago when touring the Cave. We enjoyed the Montana Grill's Buffalo burgers and jalapeno cornbread. Another place we really enjoyed was a Greek place called Anna's.

My favorite breakfast spot in Nashville is the Pancake Pantry. The Gaylord Opryland Hotel is pretty awesome too. You can ride a boat thru the lobby.

I think what I will do is hit The Hermitage first thing. This appears to take 2 hours or so??? I might then have time for Ryman or Grand Ole Opry, or Country Music Hall of Fame(might not have enough time). Probably need to leave Nashville by 2:30. If we had an hour or two would that be enough time for Ryman, Grand Ole Opry, or Country Music Hall of Fame? Which one?

How long of a wait do you think I might encounter at The Loveless Cafe @ 8AM on a Saturday morning?

You will probably have a long wait at the Loveless on a Saturday morning.
I would choose downtown Nashville and the Ryman over the Grand Ole Opry and CM Hall of Fame. A couple of hours should be enough to tour Ryman.