well I would love to go for a dive normally but actually I'm on holiday in Europe at the moment. But if you Japanese is ok or you can get a translation check out these websites
http://www.sumoguri.com/freedivingschool/index.html
http://higedura.cool.ne.jp/
You,ll find the spearfishing where you are though around Tokyo usually done in shallow water. If you go deepeer for freediving, watch out for boats.
The Izu penisula is a nice place still pretty close to Tokyo with beautiful underwater terrain. Its worth a weekend trip.