I'll have a four-day stopover in Tokyo in July. Are there any gardens or tours anyone can recommend? I can also consider an overnight train trip during that time.

Shinjuku Gyoen in Tokyo is a famous garden. There is a pdf on Japanese Gardens linked on the lower right part of this page:
http://www.jnto.go.jp/eng/location/rtg/index.html

You might also look at the pdf about Enjoying Bonsai and Horticulture.

Info on gardens is here:
http://www.jnto.go.jp/eng/location/i...s/castles.html
and here
http://www.japan-guide.com/e/e2099.html

Hamarikyu is lovely and right in Tokyo next to the water of Tokyo Bay and the Sumida River.

In central Tokyo, you could find two very beautiful Japanese style gardens: Rikugi-En (18th century) and Koishikawa-Korakuen (17th century), walking along the serene landscaped winding pathes, it will be hard to picture the busy city outside.

In July, the rose gardens in Kyu-Furukawa Teien will be in full bloom, but it is more of western style, although is warthwhile for visit two.

Second the two gardens mentioned above. For Hamarikyu Onshi Teien, it would be fun to visit the famous Tsukiji Market(not just for fish, huge traditional japanese market all around) in the early morning, have something interesting(not only sushi) to eat and buy, then a short walk(less than 10 minutes) to the garden.

All gardens (total about 10) could be easily reached by public transport, details are listed on the Tokyo tourist map (pink one) handed out by tourist centre. Or you could check: www.tokyo-park-or-jp/english/index.html.

Thank you all for your thoughtful and detailed replies. I definitely have enough info to enjoy my trip! I wonder if the roses suffer from Japanese beetles there, as mine do here? I must go see!

Yes, you must! and please report back with your findings.

We don't have roses in our own garden, but nearby is a big public rose garden with hundreds of rose bushes. Never seen a Japanese beetle there...but I'll bet it's because insecticide is used liberally and often.

If you're going in July, it could be hot and humid. Second Rikugien, Shinjuku Gyoen, Hamarikyu. Good point about Furukawwa Teien--just check when they'll be open. I also recommend iris garden near Meiji Shrine--it should be in full bloom.