I’ve been findinglooking for new Japanese high schools, but I still haven't found a good one yet. I’ve been looking for new Japanese high schools, but I still haven't found a good one yet.

"Finding" is a verb which sounds weird here. I think it's because it's usually used more in places where the discovery is accidental, or not intentional. Eg: "I've been finding my neighbour's dog in my yard." or "I keep finding sand in my clothes after I went to the beach." Because you are actively looking for schools, you should say "looking for" or "trying to find" or "searching for".

I’ve been finding new Japanesesearching for a new high schools, but I still haven't found a good one yet. I’ve been searching for a new high school, but I still haven't found a good one yet.

探す = to look for, to search for 見つける = to find I don't think you need to say "japanese high school". We never say things like "american high school" when you live in America or "british high school" when you like in Britain. You can just say "high school".

Kanagawa, where I’m going to live, has a weird school system, so maybe I can’t go to the high school I want. Kanagawa, where I’m going to live, has a weird school system, so maybe I can’t go to the high school I want.

Just needed a second comma here