I think you're supposed to not like Dany after awhile. At first she kicks ass because Khal Drogo and her relationship with him is awesome, and then her dragons as well and her clearly magical existence, like literal magic. But then after that story ends and we move on to her fucking around while all of the other stuff happens in Westeros, she's just doing nothing. Yeah, sure, we get some neat scenes with her ending slavery and what not and building a massive freed slave army which is cool, but it's still just a whole bunch of scenes of her floofing about doing nothing of importance. In the grand scheme of things it's massively important, but for literal years in the books and the show, nothing of consequence happens that really affects the other storyline. With the head of the King's guard who leaves to be at her side instead of serving Joffrey, sure, there's some bleed through, but that's the Westeros stories affecting her, not the other way around.
So, anyways, I said a lot of random shit. Point being, she can kick ass and can be interesting, but at the end of the day, she's doing nothing until George R.R. Martin pulls the trigger and just send her over to Westeros.