For the nerd in me, here is what I liked about Twilight:
Each vampire seems to have a special power in addition to just being a vampire. One can read minds, one can see the future, one has enhanced hunting senses and strength and speed to back up that hunting, etc.. Essentially it makes for an interesting adventuring party, without everyone being the same class.
Vampires can and do fight other vampires, and the fight scenes are pretty good. Lots of stuff breaking, and some nice wire work for jumping from tree to tree and such.
Vampires often live in the pacific northwest, because it is overcast all the time, hence they can go about during daytime hours without much trouble. They are not harmed by the sun in this version of vampirism, they just glow in a bit of an alien way, which would call a lot of attention to them if humans saw it.
A particular vampire "family" lives in a nice big house with large open windows, and they call themselves "vegetarians" because they do not feed on people, just animals. They seem to spend a lot of time reading and listening to music and jumping around in the trees in the forest, since they have a lot of time on their hands given they never sleep (and they own no coffins, and have no trouble with religion, or garlic, or being invited into a house).