Our answer is simple,just do as the Japanese people do. It is too hot to make a round trip or stay in big cities in summer,but you can enjoy summer festivals everywhere in Japan besides famous festivals such as Gion Festival in Kyoto,because almost all shrines will hold their own summer festivals.
There are also many seaside and mountain resorts in Japan where you can enjoy Japanese summer with local people. Don't hesitate to visit resort places where not popular for foreign tourists.
We recommend Ushimado in Okayama prefecture as seaside resort where you can enjoy many kinds of water sports and experience Japanese tradition and culture.