Eh, nothing that he's every written about Dany has exactly enthralled me. I love all the other characters, but Dany is so boring. If I didn't believe she was of paramount importance somewhere down the road, I'd skip her chapters entirely. As it is, I just grit my teeth and push through them because the other bits are interesting enough.
Whatever her storyline is, I hope Martin gets to the point soon. I also hope that she doesn't end up becoming queen of Westeros. I have to say, I'll feel more than a bit cheated if the whole series climaxes with that.
She isn't evil or anything (she actually seems to be fairly decent), but I just can't cheer for her, even in a small way. I'd be happier if she only got one chapter per book, or better yet, just showed up in Westeros fully "formed" and ready to be defeated as yet another threat.
Any of the Starks are interesting, as is Tyrion. Hey, even Jaime is more interesting than Dany. Any of them could carry a whole story themselves and hold my interest. I do have to say, though, that Jon and Arya are my favorites.