I can only assume that they wanted to be buried with other members of the fellowship, but unfortunately only one was left, and that was
Aragorn.
Frodo and
Sam both left on
ships for
Valinor, as did
Legolas,
Gimli, and
Gandalf, and
Boromir died much earlier. Not to mention that they would be much more honored and remembered well if buried in
Gondor.
The Shire knew virtually nothing about their heroic deeds in the
War of the Ring apart from helping clear out the Shire when they returned, but it wasn't like they were going to be remembered forever there, so they probably went somewhere that they knew they'd be rememebered forever.