I think Mai HiME might be what you are looking for. It takes place in a highschool, the characters who are in love don't like each other much at first, it has a serious plot (albeit that's evident mostly in the second part of the series). But it also has a lot more female than male characters so techically you could call it a harem but I don't think it actually is one. There is a lot of fighting, too. Well, if you ask me the romantic parts suck quite a lot but maybe that's just me.
