The Grey Havens
 

Just a few questions:

What were the Grey Havens?

What happened to Frodo Baggins and Samwise at the end of the LotR?

Did he go back to the Shire with the rest of the Hobbits? If the Hobbits went back to the Shire?

The Grey Havens were the West-havens of the Eldar, in Lindon. There, Círdan the Shipwright built ships for the Eldar escaping Middle-earth to Valinor.

Frodo, Sam, Bilbo, and the other Ring-bearers (as well as Legolas and Gimli, later) went to either Tol Eressëa or Valinor.

Ok so, did they ever go back to Middle-Earth, back to the Shire? or was the Shire destroyed?

At the end of LotR, Frodo and Bilbo depart from the Grey Havens. Sam, on the other hand, goes back to the Shire for awhile before he too, departs. Awhile meaning long enough to have a family and a living. I can't remember exactly when Sam left though. If I find it somewhere, you'll find it here in .2 seconds!

Ok thanks, I think I have everything I wanted to know. So Bilbo & Frodo go to the Grey Havens, and then the Shipwright dude builds them boats and these people along with Frodo and Bilbo leave the Grey Havens and go to this place called Valinor. And Sam goes, gets married and has children in the Shire, and pretty soon goes to the Grey Havens and then to Valinor. Right?

Pretty much right. I'm still trying to find exactly how many years went by before Sam departed.
I know, let me go look at the Tale of Years...that should have the answer.
Here it is! Sam left in 1482 after the death of his wife. So that would be (roughly, don't trust my math skills) 63 years after the LotR took place.

The facts are pretty much right, but Frodo, Sam, Bilbo, and Gimli didn't go to Valinor. They couldn't set foot in Valinor, for they were all mortals. They ended up in Tol Eressëa where they lived out the rest of their days, the Ringbearers being finally healed of the burden of the Ring.