Getting a scholarship in Kyoto, have to choose 3 months between April-Dec.

Getting a scholarship in Kyoto, have to choose 3 months between April-Dec. Stay is covered.
I wan to focus on cheap travel, exploring museums and natural beauty. Meeting fellow researchers( I am a student) which three months will be best. I am thinking either Arpil-June or Sep-Nov. Want to avoid extreme cold or heat. What are your thoughts?

by Fun-Fun9855