Seeing geisha today is like getting a glimpse of a long-gone past. They have become such a rarity that even most Japanese never get in contact with them.
The largest remaining population is present in Kyoto’s premier geisha district Gion. In the evening, when geisha are on their way to dinner appointments with clients, the chances are that you will spot them on the street. Failing that, you can see them first-hand at public shows like Gion’s Miyako Odori (dances of the capital). This is an arrangement of traditional music and dances, painstakingly choreographed and performed by more than two dozen geisha and maiko (geisha in training).
During the day, you may see a number of young women who look like geisha but are not. Dressing up as a maiko has become a popular activity in recent years. Telling the wannabees apart is easy. True geisha neither take selfies, nor do they pose for tourists on the street.
Seeing cherry blossom is no less tricky: Full bloom only lasts for about a week. The short-lived nature of the blooming makes it a perfect embodiment of mono no aware, a concept in Japanese philosophy that refers to the impermanence of life. It seems as if the appreciation of cherry blossom in Japan is not motivated by its visual sensation alone.
Assuming that you plan visiting the main tourist areas around Hiroshima, Kyoto, and Tokyo, I suggest that you start your journey in Tokyo. Arrange for an arrival there at the end of March, then continue with your route westwards. This itinerary worked out perfectly well for me on two trips; it is also backed by meterological records. Furthermore, I recommend that you check out japan-guide.com’s daily reports and other blooming forecasts when finetuning your itinerary.