One thing,
elempi. Shouldn't you have discerned
Men and
Dúnedain? Just a thought.
For me... well. Using an elimination method, I would say who I don't identify with: the Hobbits and the Dwarves (sorry Agan... but it's not for the reasons you mention). The immediate thing, and I believe many of my friends would think so, is an Elf. Though personally, I am not so sure. I
would say Elf because I like them, why not, and I have certain Elvish traits no doubt - the sort of a melancholic, fantasy-view and dream-weaving, but there are other things that restrain me from it. I am not probably that much tra-la-ley

and not that im-mortal(meaning: not that distant from mortal things). My
no to the Elves is totally opposite to that of
elempi's: I cannot be Elf because I am too tied to the reality of the world, here is my place and I have to be here.
Now I know some would like to see me confess to being an Ent, but in fact, when someone asks me about races in ME, I would think about Hobbits, Dwarves, Elves and Men (and Dúnedain), but not Ents, so... I don't know. And I don't think, given the question, that I have most Entish traits either.
So, it looks like Man for me. Had there been that Dúnadan option, I wouldn't have taken it either: I feel myself more amidst the "common folk". All these Easterlings in Beleriand (the good ones), Breelanders and Dunlendings, people of Nurn, men from the White Mountains... I like Northerners but I am probably not one of them. Only that...
...there is one race still. I don't know how it may sound: funny, nontypical, maybe it could seem arrogant from certain point of view. But I feel that maybe this is the race where I'd feel most at home, whose traits are the closest to me. Again, please, do not interpretate it the way that I am arrogant or something like that. That "race" is the Wizards.
But it will be on everyone to judge if that's plausible