Ooh, fun. Here are some bonsai destinations that come to mind.
Depending on the season, there are good bonsai exhibits to visit:
- January: Gafu-ten (shohin bonsai, Kyoto)
- January: Sakufu-ten (high-level show, Tokyo)
- February: Kokufu-ten (Japan's best annual show, Tokyo)
- May: Satsuki azalea shows in Tokyo and Kanuma (Tochigi prefecture)
- November: Taikan-ten (great show, Kyoto)
For bonsai pots, stop by Bonsai Pots Marutatu and nearby kilns in Tokoname (outside Nagoya, a day trip from Tokyo).
As for non-bonsai visits, any place you've heard of is pretty great. Kyoto is definitely worth a visit if you want to experience famous Japanese gardens. Do note that the city is very busy in fall when the maples are in fall color. Here are some photos of selected Kyoto temples: https://bonsaitonight.com/tag/kyoto/ and here's a resource for finding them: http://kyoto.travel/en/shrine_temple
If you can make it to Kokufu, walk around Ueno park - the park in which the exhibit is held - and be sure to explore the nearby pedestrian mall (Ameya Yokocho) just south of the Ueno train station.
The Shibuya and Shinjuku neighborhoods are obvious Tokyo fun spots to visit in the evening.