ouran high school host club is one of my all time faves. available all volumes in english and completely scanned. girl is pretty awesome and guy is just well... funny
girl got game is really funny. involves sport but it's not really an action manga. same status aas above. girl is super funny. bit thick but definitely not innocent
akuma to love song is okay too, but not one of my absolute favourites...not yet fully scanned
chihayafuru is pretty good, that is if you don't like josei but it's not nearly complete unfortunately. girls is quite thick but smart when it comes to karuta and friendship i suppose. one of those girls who never really gives a thought to romantic relationships.
hoshi wa utau is close to completion but it's more about unrequited love
koi dano ai dano is REALLY good but not near completed unfortunately...smart girl character
hana kimi i havent read it but have heard good things. completely scanned
oresama teacher is my no.1 at the moment. i don't know about it being close to completion but the scanlator is pretty consistent with her blog and updates
strong girl character though academically, a bit thick. guy is definitely not conventional. don't be put off by teacher student thing because it's really not like that.
bus hashiru is a collection of really cute oneshots. slightly cliche but that's alright cos they're all oneshots. completely scanlated. there are about four volumes, all of oneshots!
beauty popperhaps? completely scanlated nd i'm pretty sure you can get in english. girl is mentally strong and can beat the boy at his own game as well
Otokomae! Beads Kurabu complete. unique characters. though it's not long, just a oneshot.
dengeki daisy is good too but not completed.
all of them aside from where i've pointed out, are more than 5 volumes
as you can see, i've read my fair share of high school shojos
