I'm very glad you've taken abmj-jr's advice about the humidity in July to heart, eefor jfp. You will already have a better time in Japan because of it.

How you handle the weather is going to have a huge impact on the kinds of things you'll want to see and do. What might be a pleasant half an hour walk in the Spring or Autumn could be an unendurable ordeal in July, so the sightseeing suggestions I might give for an April trip might be terribly unsuited for a July one. If you are going in the first two weeks of July then I would suggest looking to a dinner at the Ukai Toriyama as they release fireflies into their grounds at this time of the year. You could combine this with the relative cool of Mount Takao, a beautiful area to hike in and a refreshing change from the city.

I have to admit that I have always steered well clear of Japan in the summer, but early June has given me enough of a taster to know how exhausting usual itineraries are. Personally, I'd fill up my days in the city with visits to large museums with climate control and take it very, very easy otherwise. To be honest, I'd probably go North or into the Mountains given the choice. I can deal with 48C temperatures in Madrid, but the humidity of somewhere like Kyoto and Tokyo is not something I can be active in.

Good luck!