If you were an elf, would you go to the Grey Havens or stay in Middle-earth...

[Galin]

Originally Posted by Elmo

If you are of the Umanyar, you are not reincarnated. Once you die you stay permenantly in the Halls of Mandos. (...)

I don't recall this myself. Maybe I'm off but maybe you're thinking of the idea that those Unbodied Elves who refuse the summons of Mandos -- that is, Elves who had died but refused to go to Mandos in spirit -- were not allowed to be re-born. At this stage Tolkien still imagined that Elves were reborn as elf-children incidentally, but he ultimately abandoned this form of reincarnation.

I think it's mentioned in the same book the the Umanyar don't even speak to the other Elves in the Halls.

The re-born reported that there is little communing of kind with kind, or of any one fea with another, for the houseless fea is solitary by nature '... and turned toward those with whom, maybe, if formed strong bonds of love in life.' Morgoth's Ring

Originally Posted by Eorl of Rohan

Well... Sooner or later, all elves have to leave middle earth. There is no choice. The fourth age is the age of Men, and elves have no place - they must either go to Valinor or fade away and die - who would then go to the Halls of MAndos and then go to Valinor later on.

As noted, Elves who die can refuse Mandos and remain in Middle-earth. Morgoth's Ring also mentions the Lingerers (faded Elves), but fading in the body does not equate to death.