You mentioned Spring. Avoid (like the plague) the first two weeks of May, starting maybe April 29 or 30. They call it Golden Week because there are several holidays one right after the other, and everyone takes the time off and travels back to their original home town to see their families. Every train out of town is full to bursting, and nothing is fun.
Having said that, the first couple of weeks in April should be perfect for cherry blossom viewing. The last time I was there I got kind of tired of them, they’re everywhere, but if you haven’t seen them before you’ll be fine. Weather will be a bit cool, between 15 and 20 C, but nice for walking around.
I really recommend Kyoto, especially during cherry blossom season. My three favorite temples are Byodo-in (serenity and symmetry), Kyo-mizu-dera (up on the hill, great views, majestic) and Ryoan-ji, the zen temple with the famous rock garden. Also by all means see the Kinkaku-ji, the Temple of the Golden Pavilion. This can all be done in one ambitious or two leisurely days. Also, going to Kyoto from Tokyo will give you a chance to ride a bullet train (Shinkansen, not cheap, but a very Japanese thing to do). If you’re doing two days you can also go to Nara and see the Great Buddha (Dai-Butsu) in Todai-ji temple, and the tame deer in the park – you can feed them.
If you and your daughter are comfortable with such things (i.e. being naked among other people of the same sex, of varying ages) try an onsen. You could stop at Odawara on the way to Kyoto and find one there. You don’t have to stay overnight to have the bathing experience. Read up on bathing etiquette before you go so you know the ropes. No soap in the soaking pool!
If you don’t want to take the time for the previous two paragraphs, you can take a day trip to Kamakura, an historic military capital, a couple of hours south of Tokyo. They also have a Great Buddha (not as big) that is outside, tons of temples and atmosphere, and you can probably find an onsen there as well.
Note that Japan is making great efforts to make foreigners more comfortable, due to the 2020 Summer Olympics. You should get a lot of the benefit from that.
Good luck and have fun.