Well how old is Chibi-Usa physically in your fic?
We know that Furinkan has a pre-school because Midori (the teacher Happosai fell in love with) worked there.
There was also the two kids who thought Happosai was Santa Claus (I don't know how old they were though.)
hmm. Furinkan (or any one of the neighboring also fictional towns from the manga/anime) likely has its own primary school. But if you want something from another manga or anime... the only ones I can think of that take place in Nerima Ward are Nerima Daikon Brothers and All Purpose Cat Girl Nuku Nuku. Neither of which feature an elementary school. ...well NDB might but I don't think so.
EDIT
wait.
St. Hebereke's School for Girls (named St. Bacchus's School for Girls in the manga, which is mentioned as a nickname in the anime)
the wiki calls it a Catholic unisex high school.
But you could say that the same church runs a primary school too.




