The Kyoto Visitor's Guide website has released it's April event schedule, and there are some great things to see and do in Kyoto this month! Check it out HERE.
My personal recommendation are the geisha dance performances that are going on this month in the Gion and Miyagawacho neighborhoods. This is a once-a-year event that is meant to show off each neighborhood's maiko (geisha in training). I attended one of these shows last year and it was really amazing. Highly recommended if you can get tickets.
Some of last month's light up night events continue at various temples in April, and I previously wrote about them HERE. Definitely worth checking these out if you want something to do after dinner one evening. Kodaiji at night is an amazing experience!
Don't forget about the flea markets. Kitano tenmangu has a huge market every month on the 25th, and bargain hunters can spend all day there looking through all sorts of interesting treasures.
The rainy season will be here before we know it, so enjoy spring in Kyoto!