I am all for spontaneity but with 3 of you I'd think some reservations would be a good thing. The nice thing is that even if you book rooms in, say, Osaka or Kyoto, with a Rail Pass those cities make very good home bases for explorations farther afield. Day trips abound - Kyoto -or- Osaka, Nara, Hiroshima, Himeji, Kanazawa and many others.

You should be aware that June is the monsoon (rainy) season and be ready for rainy days.