This is probably the most important thing to think about when thinking about ways to fix Twilight. It’s a vampire love story, so vampires would logically be at the heart of it. Their characteristics, to be more specific.
Vampires in the Twilight series are deathly pale, are much stronger and faster than humans, and are virtually indestructible. The only things that can damage them are other vampires and the Quileute shapeshifters. Actual werewolves (or Children of the Moon, as they are referred to in the series) probably could as well, except they were hunted to extinction by the Volturi.
However, there is one particular characteristic that makes Twilight vampires stand out, both literally and figuratively. To sum it up, when a vampire goes into direct sunlight, it bounces off their skin, making them glisten, sparkle, whatever word you want to use, as opposed to incinerating them like in traditional vampire lore. This one characteristic is a major turnoff for vampire fanatics, to the point of where they don’t take the Cullens seriously, even though they should. What’s ironic is that those moments we see it happening are few and far between, happening only once in each book. We probably see more of it in the films than we do in the books.
But, I digress. My idea for this is fairly simple: Alter the vampires to make them more acceptable. The first alteration should be obvious. Take away the sparkling. You’d be surprised how many people would love that. Another alteration I would make is to make the vampires vulnerable to sunlight until their skin builds a tolerance to it, whether through exposure or over time. Another alteration would be the re-introduction of the stake as a fatal weakness. Of course, it has to go through the heart and it can also be anything with a sharp point, like a broken tree branch or a sharp rock. Yet another alteration is the ability to also consume human food, which does help reduce the thirst for blood somewhat. Aside from also downplaying their speed, strength, and durability and adding fangs, that’s all the changes I’d make. I’ll discuss dhampirs (human/vampire offspring) in another post.