Oh, gentle reader! This is the sort of question that gives Molly and Jenn many feels.
If we can say so without being obvious, please, go forth and Lord of the Rings-ify yourself. (It’s totally ok to skim the songs and the parts with all the walking, but if you love Martin’s descriptions of everything, well, Middle Earth is a good place to visit.)
For an epic, sweeping story arc, look to Robert Jordan’s Wheel of Time series (first in the series is The Eye of the World).
For non-medieval-European-fantasy full of magic and violence and lovely imagery, pick up N.K. Jemisin; start with The Killing Moon.
For super-sexy, super-political alternate medieval Europe, try Jacqueline Carey’s Kushiel series (Kushiel’s Dart).
For intrigue and dragons and bastard sons and conniving royalty and unforgettable characters, you cannot go wrong with Robin Hobb (start with Assassin’s Apprentice).
Ursula K. Le Guin’s Earthsea books are not at all like GRRM’s books, but they are astonishing, vital, mythical fantasy reading.
If that is not enough to start, we can also talk about Tad Williams, Melanie Rawn, Jo Clayton, Patricia Kenneally, Raymond Feist, David Eddings, and a whole lot more. But these should get you started!
(We would now like to curl up with some hot cocoa and a big fantasy tome ourselves.)