Greetings to you too! Welcome to the Lex!
I think that if you are not trollish, you will find people generally more than willing to talk about what they like about Twilight here ... most of us are here because we have few if any people in our offline lives to talk to about it.
The Unpublished Author wrote:find out if my dislike for it stems solely from my existing outside the demographic the series is trying to appeal to.
When Stephenie has talked/written about writing Twilight, she has been very clear that she originally wrote it simply for herself, with no conscious intention to turn it into a novel at all, and was shocked to actually sell it. So I don't know that it was really meant to appeal to a specific demographic, and certainly Breaking Dawn busts out of what I would usually consider a YA novel. I would guess that it appeals to fewer men than women because it is, at heart, a romance, and it relies heavily on dialogue. There are times when it reminds me of Austen's books, because there are long stretches where so little happens ... until the fantastic explodes across the page. You will find that fans agree that her writing style has flaws and her copy editor appears to have over-relied on SpellCheck (there are threads on this here), so she will not appeal to you if you require a sophisticated writing style. I don't. I read for character. If the character interests me, I will read them ... if not, then not, no matter how good the writing technically is.
I hope you enjoy it here. Congrats on finishing a story - I never have! There are also threads for writers here, with what look like some interesting discussions.