Normally the end of Mar to the beggining of Apr. However, actually depends on where you will go. IF you go to Hokkaido, Sakura season will be from the end of Apr to the beggining of May.
I asked last year to Japanese guides. If you want to get real local information, I recommend to you visiting there page:D
- What is your favorite season in Japan and why?
- What are your tips for vegetarians in Japan?
- Hanabi season (fireworks season) in or around Tokyo. What hanabi event do you recommend and why?
- Where can we find discount coupons or deals for restaurants and shops?
- What are some useful train etiquette tips, both in the station and on the train?