Whilst I appreciate that this is a golden opportunity for your family and that you will want to pack in as many experiences as possible, please bear in mind that from the second week of June onwards you can expect it to feel rather warmer than the actual predicted temperature might suggest. The humidity levels, even on a dry day, can really sap away at your energy levels.
When planning itineraries do take care not to schedule in too much in a day, getting around on foot may well take more out of you than you expect, and take care with your wardrobe; thin, light clothes that let you perspire and which dry out quickly, same with footwear (and take spare socks around with you as there will be places you'll want to visit which require that you remove footwear - you will want something dry to slip clammy feet into). A tip from my Japanese husband on drying out shoes overnight: Shred newspaper into strips and push a generous amount into your soggy footwear. Also, Japanese deodorant is way less effective than Western equivalents, make sure you bring plenty!