Having lived there for 2 years, I can suggest a plethora of places to visit.
16 days is not a lot of time, how are you splitting up your time between Tokyo/Kyoto/Osaka?
If you are flying into Narita and also out of Narita (necessitating a round trip to Kyoto and back), then I would suggest a JR pass and then taking the shinkansen. However, if you are flying into Narita and then flying out from Kansai, then the JR pass may not be necessary (check the costs; a round trip shinkansen ticket from Tokyo to Osaka is about $350).
Unfortunately, during this time, there is unlikely any outdoor farms that will be open...however, there are lots of stores in the Tokyo and Osaka area. If you are going to be doing shopping for equipment, I would suggest you look around the stores first; different stores will often have cheaper prices/discounts on ADA equipment (cheaper than MSRP).
Of course, other than stores, you can always check out Japanese gardens as well as temples. This time of year is excellent, particularly in Kyoto due to the leaves changing colours.
Yes, please do give shout out of any places, it'll be my first visit to Japan.
Im definitely keen on shopping for equipment, I'll be going to most of the big shopping department/area. Can you suggest any dedicated aquascaping stores?
I'll be in Tokyo for a week then train down to Osaka and spend the remaining time there and fly home from there too, so a JR wont be necessary.
I'll bring back shrimps......; any shrimp favoured food products I can find!