Personally, I don't understand the confusion with elves.
Elves are not like Spock from Star Trek. They aren't emotionless, drab, and boring. If anything they are the opposite. The First Age was rife with emotion, and not all of it was good. There were "bad" elves. The Sons of Feanor were so consumed by lust and revenge, they killed their own kin, stole their ships, and set fire to them, leaving a good deal of their comrades stranded in the deadly cold. Their was lust, deceit, jealousy, anger, despair, and sorrow. There was also great joy, beauty, and wonder.
Elves are immortal, yes, but they are people. Age and experience, especially when proportioned with the brevity of human life, can make one haughty and proud with a touch of melancholy, but there are still friendships and happiness and wine. Lots and lots of wine.
Imagine being 5,000 years old. Yes, I would want a drink too.
My suggestion to make it a little easier, and to be able to relate to your own character a little better, is to stay away from firstborn. Go with someone a little younger. And by younger, I mean less than 1,000 years old. An elf like that is still an elf, but is maybe easier to relate to. They have not witnessed firsthand the tragedy of Beleriand's fall, or the treachery of Sauron.
Mirkwood Elves are a particularly good choice, I think, because if you read the Hobbit, they basically party in the woods. Many of them are Nandor, who never visited the undying lands, or had much at all to do with Beleriand, so one might even dig a little deeper and go with an older soul who is only now venturing out to discover the other side of the Misty Mountains. What are humans like anyway? Who are these bizarre little people, and how do they stay so little by eating so much? You get the idea.
There is, however a touch of xenophobia among elvenkind. They don't trust men, much less Dwarves, and Hobbits have barely been a blip on their radar. That said, everyone is fighting for a common goal, and elves know what side they are on.
I myself play this way with my Hunter, who is an elf of Mirkwood. She's really just a kid (only 250 years old or so) and she parties with Hobbits and laughs at how silly they are. You don't have to be somber and arrogant all the time. (But you can if you want. There are certainly enough of those.) Relax and hang out with the Humans and Hobbits, (and Dwarves if you can stomach them), and at the end of the day you can be pensive and melancholy while they're all sleeping off their hangovers.
"These goblins don't seem to appreciate my new bow. How sad. Perhaps if I give them some more arrows..." -Farothwen Lhûgonnen