Personally, I rather like the fics that focus on the vampire siblings and their pasts, because frankly, they're far more interesting. Try these fics:
Brotherhood (http://www.fanfiction.net/s/4169295/1/)
Cowboys & Indians (http://www.fanfiction.net/s/4434193/1/)
Rosalie's Revenge (http://www.fanfiction.net/s/3919836/1/)
Tie Me Down to this World (http://www.fanfiction.net/s/4834902/1/) (All-human AU)

And maybe these authors in general (IDs are for FFN):
* Brynna (id: 180630)
* Chicory (id: 2065315)
* EliseShaw (id: 1775901)
* Eowyn77 (id: 1318747)
* Kristen Elizabeth (id: 3997)
* whitereflections12 (id: 1153791)

You might like them, might not. Either way...

(Sorry the links are loose - I'm in a rush (always am, lately) and don't have time for fancy html.)

You've come to the right place! Here are some of my personal favorites:

The Meadow Scene Redone by Aradia Lestat-Ming Ue
-Takes a specific scene in the book, and gives it a different spin, one that is much better than the original.
http://www.fanfiction.net/s/4759768/1/TheMeadowSceneRedone

The Paper Doll Kindergarten by LingeringLuminosity
-A delightfully dark and creepy take on an already screwed-up character.
<a href="http://www.fanfiction.net/s/4516602/1/ThePaperDollKindergarten">http://www.fanfiction.net/s/4516602/1/ThePaperDollKindergarten

Friday's Child by Lise
-...On the other hand, this takes a certain character and gives them more depth.
<a href="http://www.fanfiction.net/s/4450121/1/FridaysChild">http://www.fanfiction.net/s/4450121/1/FridaysChild

moves in mysterious ways by Lisse
-Takes a different spin on the Twiilight-verse... with a different outcome.
<a href="http://www.fanfiction.net/s/4333491/1/movesinmysteriousways">http://www.fanfiction.net/s/4333491/1/movesinmysterious_ways

And in return, I'm off to read your recommendation.

(Why, oh why can't the real stuff be like this?!)