The classic space is definitely Archive of Our Own, no question. It's got a tagging system that's unparalleled for a specific ship like Jacob/Edward, which means you can filter for exactly the tropes you want—enemies to lovers, wolf/vampire power dynamics, pack politics. The quality control feels higher, too; you find fewer abandoned stories from 2009 and more recent, finished works because the culture there encourages completion. I remember sorting by kudos and finding this incredible, novel-length reimagining where Bella was just a side character and the main conflict was about territorial rights in the Olympic Peninsula. It felt so much more mature than the old stuff.
I'd be remiss not to mention some dedicated Twilight fanfiction archives that are still limping along, like Twilighted. The archives there are a treasure trove of pre-'Fifty Shades' era fandom, pure and unadulterated by later trends. The writing style can be very of its time, all script format and songfics, but there's a raw charm to it. That said, for consistent updates and community interaction, AO3 is where most of the action has migrated. The comments sections on popular fics are vibrant, and you can easily track an author's other works if you like their take on the pairing.