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We would be more than happy to show you some great dives down this way in April. Water temp is now 70F or so and climbing by late April should be up a few degrees.
You mentioned that you only have a morning and and evening to dive while you're here. Realistically from Tokyo you need at least one full day to make it worthwhile.
To get to anywhere that's worth diving, the closest place is Atami, just on the north-east corner of the Izu peninsula. You can get there by Shinkansen (Bullet Train) from Tokyo in about an hour and a half. If you planned carefully, you could leave Tokyo first thing in the morning, get out to Atami, get two boat dives in and get back into Tokyo for maybe 6pm.
There are closer places (like Enoshima) but they're inside the Tokyo bay, and really is not worth bringing your gear over for. Also, you'd need to take local trains, so your travel time might end up being the same anyway (although cheaper)
What are the dates that you're going to be here?
If you have 2-3 days then the possibilities open up quite a lot. There are many locations on the Izu peninsula (Tago, Mera, IOP, Kumomi, etc), or as suggested, if you can get down to Okinawa, the conditions would be much nicer.
A good web-site to check out is Padi Japan, they list links to dive spots all over the country which usually list conditions at the local dive sites.
You could pop down to Okinawa while you are here, 2.5 hour from from Tokyo. There conditions should be 30m + viz and 23/24 degrees water temp.
I was doing some research and apparently there is no direct train to get to okinawa...I have to go to hakata and then take multiple trains to get there...I have been told...do you know if there is a direct bullet train to Okinawa..heard that is the best diving