Many visitors to Kyoto have two items high on their priority list: seeing geisha and cherry blossom, respectively autumn foliage.
A great place to watch autumn foliage are temple and shrine gardens. Kyoto has hundreds of them dotted throughout the city and its forested outskirts (see my favs on Google Maps). During autumn, the crimson tones of the Japanese maple dominate the scale to such an extend that the term for it (momiji) has become synonymous with leaf peeping in general.
When visiting Japan it is relatively easy to hit foliage season, as it lasts for about 4–6 weeks in each region. The best time for the main tourist areas around Tokyo, Kyoto, and Hiroshima is the second half of November. For more details check out the autumn color reports from japan-guide.com.
Seeing geisha is a bit trickier. Over the last few decades their numbers have been dropping visibly. The largest population of geisha and maiko (geisha in training) remains in Kyoto’s premier geisha district Gion Kobu. Chances to spot them on the street are best in the early evenings, when they are on their way to dinner appointments with clients. Failing that, you can see them first-hand at public shows like Gion’s Miyako Odori (dances of the capital).
During the day, you will see a number of young women who look like maiko but are not. Dressing up like a maiko has become a popular pastime for tourists. Telling them apart is easy, however. True geisha, usually on a tight schedule, do not have time to pose and take selfies. They are unlikely to stop for you to let you take a shot of them.
Hitting cherry blossom is probably the most challenging. The cherry’s petals are so fragile that full bloom lasts for just about a week. Its delicacy even gave the blossom a role in Japanese philosophy, as a symbol of life’s impermanence (mono no aware).
Assuming you plan to visit the main areas around Hiroshima, Kyoto, and Tokyo, I suggest that you start your journey in Tokyo. Arrange for an arrival at the end of March, then continue with your route westwards. This itinerary worked out perfectly well for me on two trips and is backed by meterological records. There are even forecasts for the blooming, and again the reports from japan-guide.com are worth a look too.
Kyoto is a bicycle city. Many places of interest are within a radius of 5km or even less. Since the city’s street layout is based on a grid pattern, negotiating your way is easy. You can resort to many low-traffic, one-way backstreets, thus avoiding busy main roads. There are bike rental shops throughout most of the city.
For longer distances, you better use rail services. A great deal for accessing the city’s eastern districts is the one-day pass from Keihan Railways for ¥500. Hankyu Railway, which lines go as far as Osaka, is offering another attractive one-day ticket for ¥800.
There is an extensive network of local buses too. Kyoto’s congested thoroughfares, however, make using it less efficient. Hiring a car is no better. It is rather expensive, around ¥5,000–10,000 per day and may require some unusual paperwork (e.g. a Japanese translation of your driver’s license).