Hi Kevin,
June seems to be the start of the rainy season, so at least go prepared. But as someone replied, Kyoto is definitely worth a couple of days. We visited Japan this past October and spent 3 nights in Kyoto. Looking back, we could have stayed another day or two. It all depends on what your sightseeing pace is. And even a week in Tokyo might not be enough to see it all!
Hope you enjoy your trip!
//Eva