You know there's something like a couple of dozen of current writers right now who could reasonably be classed as having GRRM as an influence or are merely similar to GRRM and as much as I enjoyed Ice and Fire I keep never getting around to reading any of them. So uh... there's that.
I guess the most relevant recommendation I can make is this:
Miles Vorkosigan, the hero of most of Lois McMaster Bujold's Vorkosigan Saga books, is suspiciously like Tyrion Lannister (as the dwarfish child to a powerful political family in a feudal society who gets by on a mixture of status, cunning and wit). These are space opera novels rather than fantasy but... that probably... won't hurt.
Past that (or alternately if you really want some high fantasy) there's Bujold's Chalion books, similar in tone but set in a fantasyland version of Medieval Spain, with a pretty clever focus on the theology... but yes, also involving politics, low-key magic, warfare, conspiracies and unlikely heroes (the protagonist of the second book is a middle aged dowager). Either of these book series are pretty standalone compared to Martin's dense Ice and Fire series, although in the Vorkosigan books in particular there's multi-novel character development which is nice.
Speaking more generally?
As far as fantasy goes been years since I read any of his books but Terry Pratchett was a staple of my childhood. More recently China Mieville is pretty great (Perdido Street Station reads like a gritter, more adult Ankh-Morpok to me), particularly if you like your stories to be overflowing with imagination. I dunno, I generally read more sci-fi.
marillion - From the writer behind Game of Thrones comes... VAMPIRES! - for that tag line alone I'd bet any sum that it'll be a movie or a miniseries or whatever soon enough. Haven't Sci-Fi optioned Wild Cards?
