I'm usually very picky when it comes to liking characters, but... Yeah, George R.R. Martin apparently knows how to get to me. Just like everyone else, I like Tyrion, but he's not my most favourite char. I don't even know why; sure, I acknowledge the guy's awesomeness, he just lacks that certain... spark for me. It's immensely difficult to choose just one, so I'll swarm you with them instead: Jaime Lannister (his POV in books made me love him), Petyr Baelish (so deviously intelligent), Asha Greyjoy (only sensible Greyjoy, funny and badass to the core), Arya Stark (do I need to list all reasons?), Daenerys Targaryen (again, it goes without saying...)
Well, it would be easier to choose characters I DON'T like. There are two of them. Joffrey Baratheon and Catelyn Stark. Joffrey is the choice I don't need to defend, but what about Catelyn? Eh, her chapters were a chore for me to read and she isn't really that likeable. I mean, look how she treated poor Jon Snow!