Yes. One of the elf-kings held a feast near the Pools of Ivrin.

Alright, here we go then:

Umbar
Isengard
Edoras
Amon Hen
Rivendell

Amon Hen, the only place where Legolas and Gimli didn't travel with Aragorn

Nope.

Rivendel, the only place where a man didn't rule?

Wrong.

Isengard, the only place to be invaded by Ents?

Negative.

Umbar, the only place not to be visited by a Istari?

Now you're getting closer...

Guess who's back, back again...
 

Isengrim...errr..gard, the only place where an Istar made his abode. :)

Nope.

Umbar was the only one where an Istari, specifically Gandalf, did not use his power?
Gandalf threw Saruman out of Theoden at Edoras. He prevented Sauron from finding the Ring at Amon Hen. He cracked Saruman's staff at Isengard. At Rivendell he... um... helped with the flood and convinced Elrond to let the Meiadoc and Pippin join the Fellowship.

Good answer, but no.

Amon Hen, the only one where an Istari did not stay?

No. You need to think smaller.

Umbar - the only place where a hobbit hasn't been?

Correct. :)

i seem to guess 'em right these days...
 

Woodhall
Imladris
Frogmorton
Mithlond

:)

Frogmorton - the only place where the hobbits didn't meet elves?

whoa, that was extra fast!
 

I mean, I expected it to be short lived, but not that short-lived. :D

Your turn, again, Nightknight!

Woodhall gave it away...the only thing that ever happened there was the hobbits meeting Gildor and his people.

An easy one:
Erebor
Ered Luin
Nulukkizdin
Ered Mithrin

Ered Mithrin is the only one without a colony of dwarves.

Not what I was looking for.

Ered Luin is the only one that has not been sacked by a dragon or more?

You have it. :)

Minas Tirith
Doriath
Rivendell
Gondolin
the Fens of Sirion

Again, think happy thoughts.

Rivendell was the only place where blood was not spilled?

Happier than that.

The Fens of Sirion, the only one where two lovers didn't meet? (Minas Tirith - Faramir and Eowyn, Doriath - Beren and Luthien, Rivendell - Aragorn and Arwen, Gondolin - Tuor and Idril)

You're definitely on the right track, but you need to narrow your criterion.

They met lovers of another race... If Minas Tirith is the one in the First Age, then could it be Beren and Luthien meeting there?

It's Minas Tirith of Gondor, and it's not meeting lovers. You're on the right track, though.

The Fens of Sirion is the only place where a half-elf was not born.
Minas Tirith- Eldarion
Doriath- Dior
Rivendell- Arwen
Gondolin- Earendil

We don't know for sure that Dior was born in Doriath, Eldarion was born in Minas Tirith, or Arwen was born in Rivendell. And I don't think Arwen counts as a half-elf- but let's not go into that. Anyway, you're forgetting two very important people who were born at the Fens of Sirion.

Elrond and Elros! And then Eärendil in Gondolin, Arwen in Rivendell, Luthien in Doriath... which leaves Minas Tirith. Or maybe Rivendell, since you said you weren't sure of Arwen, and instead we take Eldarion in Minas Tirith.

Sorry, NightKnight, but it's not birth. Something related, though, at least in Middle-earth. But that's a great answer!

Marriages between people from different races:
Gondolin - Tuor and Idril
Doriath - Beren and Luthien/Thingol and Melian
Minas Tirith - Aragorn and Arwen
Rivendell - Elrond and Celebrian
Fens of Sirion is the OPO.

So close!!
 

Now you need to widen your criterion, and never assume anything that the books don't tell you (or imply beyond a reasonable doubt). Were Elrond and Celebrian of different races?

At least one half-elf got married in all except Gondolin?