If you go through the Silmarillion and Unfinished tales you normally find where the critical players were buried. For example Fingolfin had a cairn raised over him in the Encircling Mountains.
But where were Gil-galad and Elendil buried, given that their army threw down Barad-dur?
Elendil was orginally buried in the approximate geographical center of Gondor, atop the mountain Halifirien. He was later disinterred when Gondor ceded a hunk of territory to Rohan, and reinterred in Rath Dinen above Minas Tirith, with the other kings, his descendants all.
As for Gil-Galad, well…
From “The Fall of Gil-Galad”, as translated by Bilbo Baggins
Anyway, the Eldar apparently weren’t much for tombs, since their spirits returned to Mandos and sometimes got re-housed in new bodies.
And if Fëanor was any indication, they sometimes leave no body behind at all. Granted, ol’ Fëanor wasn’t a typical Noldor, but neither was Gil-Galad, so it’s not too unlikely he too would leave no body behind.
I’d not put Gil-Galad quite on par with Fëanor, Lightray.
I’m not aware right off the top of my head of any other Eldar who spontaneously combusted like Fëanor at death. Anyone else think of any examples?
Does anyone else recall tombs/memorials for others besides Fingolfin?
ISRT that Glorfindel was left lying on a hilltop (?) after defeating the Balrog in his first go-around in Middle-Earth. And I think Turin Turambur buried his elf-maid.
Arwen of course laid down on a hilltop and never got back up, but she was arguably mortal by that point.
Obviously, I’m away from my Silmarillion. What happened to Thingol and the other First Age elf-kings when they died? I’d expect that if any elves had tombs, it would have been they.
Fëanor was unique among even the Eldar, in no other elf or man did the flame ever burn as bright.
I do not recall any tombs mentioned, I do recall mounds with flowers raised in remembrance, but no mention of bodies being interred in them.
Jim
Finduilas was buried by at Haudh-en-Elleth, mound of the elf-maid (no bad jokes, pervs!). It was raised by the folk of Brethil.
The refugees of Gondolin did indeed build a cairn over Glorfindel’s body, on the heights of the Cristhorn, where the flower elanor bloomed.
I don’t recall reading about a tomb for Thingol, and haven’t found any references to one. Those first-agers tended to die in battle in territory which was being overrun by the enemy.
Thingol lies under the sea, of course. 
More like at the bottom of the canyon they both fell into. Are you thinking of Ecthelion?
But Thorondor the eagle dove into the abyss to retrieve Glorfindel’s body.
http://www.annalsofarda.dk/annals-of-arda/Elves-index-tables/Elves.htm
He did a lot of that in the first age.
I don’t think we can take the maker of the Silmarils as typical. His spontaneous combustion upon death was mentioned because it was so unusual.
I understand that, in the rush to pedantry, it may be possible to miss that I mentioned Fëanor isn’t a typical elf in my post you’ve just quoted there. But, really, much more of this and we’ll have half the thread parroting back part of their quote of what I said! just how many Tolkien pedants does this board have?
I’m kind of surprised that Thingol didn’t get some tomb mentioned, since Menegroth would seem to have plenty of room for one (what with the thousand caves, and all), and since Melian was around for a little bit after he died, giving a few last orders. Nothing mentioned, though.
However, it looks like there may have been another no-body-left-behind death: Lúthien and Beren.
Now: somebody go ahead and tell me that we shouldn’t take those two as typical. 
Yeah, but Melian headed out to Valinor right after his death, and for all we know, went straight to the Halls of Mandos to visit him! I suspect his body wasn’t all that important to her (they only did have one kid ) and I’d also suspect that the rest of the Doriathrins followed her lead in regards to that attitude. That’s my WAG, anyway.
If you’re talking about the second one for each, it’s just a matter of them leading a deliberatly obscure life and becomming lost to history, not literally vanishing. Presumably Dior took care of whatever their funeral arrangements were. The first time, though, I don’t recall what happened to Luthien, but Beren definitely died a normal human death (insofar as it’s “normal” to die from wounds inflicted by the greatest of all werewolves, though I suppose it’d be even less normal to not die from them).