Hina is a serious and dependable person, but her flirtatious side she shows to Hayate (still giggling about her "What's this, Hayate? Want to see?" teasing while fanning her chest, for example). It tempers her "serious" impression and shows that she's easily approachable, and that she's got a sense of humor.
I like her ability to make a difference and to overcome difficulties on her own.
Hina is EXTREMELY competitive and combative when she feels challenged. Tsundere = tsuntsun (mean) and deredere (kind,caring), and so far we haven't seen any "tsun" side of her yep, particularly not towards Hayate. A certain degree of tsun helps rounding out a character though, and we will be treated to that a bit later...
A character who is only dere is boring.
Emotionally vulnerable definitely fits. Hina is very emotional and very open about it - in the very first episode showing her, she got teary-eyed over the young bird in the nest. Nobody blushes cuter than her, and her mood swings from extremely happy to downcast to extremely mad are legendary. Very enjoyable to watch.
But there's more to her: She is very kind and caring by disposition, without falling into the "well-meaning but wimpy-moe" trap. She's a very good sport - see her reaction to her loss at the tournament. And most of all, she's not stuck up at all. She has all the makings and appeals of the ojousama type without the usual annoying air of superiority those characters usually exhibit.
However, what pushed her over the top and made Hina my favorite character ever will surface once we learn about her personal background, her fears and her hurts. It pains me that even though she definitely would be the best "match" to Hayate (him and her have alot in common), she still only has a total outsider chance of maybe 5% to have her "winning" in the end. Still - keep the hope alive, and her popularity count towering above the rest ^_^