Yes and no.
I'm always keen on liking female characters if they are not described as striking beauties. I hate it that every single heroine has to be beautiful (or if they aren't, it's the main point in them. Argh.) I must say this is one of the few things that consistently annoy me in Tolkien's writing, and probably one more reason why I always liked Haleth. (If someone finds a quote where it says she's pretty, I might have to change my opinion of her.

)
As to particular facial feautures etc, I'm not sure. I don't like characters with turned-up nose like mine, at least, but that's probably because they're always nit-picky and selfish and posh, which are characteristics I don't like and don't identify with (even if I have that infamous turne-up nose. Thank you, authors.)
But hmm... I do tend to be empathic towards characters with big front teeth or a gap between their front teeth... which is why I was
so angry with JK Rowling when she made Hermione decrese the size of her teeth (I quite liked a heroine with big front teeth, something not-so-ordinary) and especially with her thus allowing Hermione to transform into a beauty. I would like to sue Rowling for giving traumas to some poor young girls with big front teeth who were younger and more uncertain of themselves than me when they read that book.

Okay, I'm not that serious about it, but really, I don't approve of it.
As to other particular facial features, I don't think I have anything special to say.
In general, I don't think that looks determine whether I like some character or not, but they can add to my liking of some character. 99% only positively, but I must agree with
Agan on Hobb's Nevare.
Oh, and now I lied. I always,
always prefer brunette women over blonde women, at least in terms with sympathising or identifying with characters. It is an old obsession, one could say, and quite understandable if you take into account that I'm a brunette girl who has a blonde sister of about the same age...
And lastly, I have no particular attachement to Elrond, even though I reputedly

look like him.