Its funny hearing this sentiment so much online. Almost exclusively from men.
In my own experience every female viewer i've ever talked to finds her story the most fascinating and interesting.
Not saying one is right or wrong, but I actually enjoy her story both in the film and the books.
Series spoiler (including ADWD)
From what we've seen so far in the series, excluding the Qarth scene which felt forced as fuck, I love Dany's story. I love it up to the point where she goes 'well, fuck, time to settle down for a bit, let the people rest...' and does fuck all for a whole book being the queen of Mereen and a bad one. When she decided to marry the local because it might stop the ocasional murder i was just speechless. I used to love her storyline because of how ambitious she was, but then she turned back into what she was before she married Drogo... I do hope the little dragon-holiday will help her to become strong once again...