Having been to Tokyo both in late December and mid to late March, I'd say go in late October or early November

Echoing both nishimark and RTW1...

Late March/early April will likely be in the prime hanami time. Everything will be more crowded than usual--especially on the weekends (hotels, trains, parks, etc)--and thus, more expensive. There will be crowds and street vendors everywhere that has cherry trees. This may or may not enhance your experience. It will be a bit atypical. The weather will likely be pleasant--highs ranging from 50-60 F. The Japanese school year ends at the end of March and begins again in early April--adds a bit to the families out and about.

I was in Tokyo last week. The blossoms were just starting to come out on some of the trees. On Saturday, the canal in Nakameguro was lined with street vendors and relatively heavy crowds despite only a few trees having a few blossoms. Shinjuku Central Park on Tuesday afternoon had a fair number of groups of people enjoying themselves in the grassy areas (think picnics with booze ) despite very few blossoms out--several pop-up vendors were there, including someone doing American BBQ (smelled pretty good; didn't try it).

Late December weather will be colder. Not sure where you live--compared to say, Wisconsin or Minnesota in December, it isn't really cold at all. But it won't be as much fun visiting a temple where you need to remove your shoes before entering. There weren't a lot of tourists (but that was <cough> 20 years ago). The big concern would be the New Year holiday schedules--most of which I would expect to be posted online.

Late October/early November benefits from decent weather--still getting into the 70s in Tokyo--and a relative lack of tourists, everything else being the same. (Parts of the country will have people going to view the fall colors on the trees, but not so much in Tokyo in my experience.)

Make no mistake, during the peak of hanami in spring can be amazing (although timing it right is not guaranteed). Excusing the poorly scanned images (these were actually 35mm film, not digital), the following photos were from the Imperial Palace in Tokyo and Kiyomizudera in Kyoto. The palace crowds were as impressive as the blossoms. In Kyoto, the blossom petals were like confetti in the wind.