If you liked the Shinyuu no Mikami-kun manga, the Anime-Planet community thinks you'd like:
Tohru Honda might just be the unluckiest girl around. After a series of unfortunate events Tohru has no place to call home - that is, until the wealthy yet cursed Sohma family offer to take her in, in exchange for performing the household chores. However, soon Tohru discovers that there's much more to the Sohma family than meets the eye. Though shocked and surprised, Tohru promises to keep their secrets; but will the Sohma family approve of an outsider knowing who they really are?
The relationship between these two characters is similar to the relationship between Kyo and Tohru. Without giving spoilery details, if you liked how Shima and Umi's relationship developed, you'd probably enjoy Fruits Basket's romance as well.
Both of these are romantic one shots about new high school students trying to get noticed by their peers. The main characters are a guy and girl who begin as simply friends, but may become more than that.