she's not a grey character at all. she has no reason to be in westeros other than to conquer a land that she only has a claim to....because her ancestors conquered it. she doesn't love the dothraki or the unsullied, she's just using them as tools to get her throne. she couldn't give two shits about the people that are actually in westeros. right now it seems like the only person she cares about other than herself is maybe jon, but we will see now that he has a claim to the throne as well.

btw i don't dislike dany, i think she's a great character. and 'bad' characters can still do 'good' and/or 'decent' things. tywin was terrible in a lot of ways but kind of great in others. dany does care about freeing the slaves because she herself was basically a slave, but i'm not sure that translates to her really caring about them in a consequential way. she freed them because she had the power to do both that and pursue the iron throne - if she could have only done one of those, which do you think she would have chosen?

by martin's own 'rules', she's not a good guy. she's an agent of death and destruction who doesn't really have strong bonds with others, basically the antithesis of jon. i'd argue that she just hasn't gone full bad yet.