ASOIAF is a series about the struggle for the crown in a mythical land. It's very good if you like historical fiction and your fantasy dark and gritty. Martin also handles his female characters exceptionally well. It's worth reading JUST to see how his female characters work within the limits of their society and still manage to be autonomous. Like, I love JK Rowling and everything, but her female characters suck.
Hunger Games is worth reading if you liked Twilight. I think the thing about both those books is that they're written from the perspective of a teenage girl, so the entire book is actually written in character. I think the reason people find them cringe-worthy is because it reminds us of what teens are actually like. I mean, I would have been like Bella (minus the getting married at 18 bit!) and it's so embarrassing to remember myself like that.
You should definitely check out Robin Hobb's work. She writes in trilogies, but the trilogies continue on from one another, so start with The Assassin's Apprentice and go from there. It should keep you occupied for a while.
And have you ever checked out Bernard Cornwall's work? He writes historical fiction and fantasy and he used to be (well, technically still is) an historian so although the events aren't historically accurate, his description of the way people lived during the time period is.