Sry, good link.
Groot, if you browse all sixty-one pages of the GRRM forum, you'll find more threads on recommendations. Also, if you explicitly state why you enjoy ASOIAF, then you might get responses that point you exactly where you want to go.
I read AGOT, ACOK, and ASOS back to back to back fifteen years ago. Since then, the most enjoyable fictions I've read are Ilium by Dan Simmons, The Name of the Wind by Patrick Rothfuss, Off Armageddon Reef by David Weber, The Curse of Chalion by Lori McMaster Bujold, Legend by David Gemmell, and JK Rowling's chart busting series. I like them all for different reasons, but they all sucked me into their stories.
If you want a coming of age tale told as a memoir, the go with Rothfuss. If you want mythology, philosophy, sci-fi, time travel, Shakespeare, and war, then read Ilium. If you want sci-fi, politics, international intrigue, the Reformation, and a huge series, then Weber is your man. If you want straight forward fantasy, then you might like Legend.
I'e also enjoyed, but not flipped over Robin Hobb, Joe Abercrombie, and Steven Erikson, but many people have.
If you've never read Tolkien, Lewis, Howard, Herbert or even Burroughs, then you should partake of their works so you can know the stories that influenced Contemporary authors.