It's better to use Tokyo and Kyoto as hubs, not Osaka.

Nara can be done in an easy day trip from Kyoto (also from Osaka).

Nikko is a bit further away from Tokyo but can still be done as a day trip. There are no chain hotels in the Nikko area AFAIK, but virtually all Japanese hotels are clean and safe, so you don't need a chain hotel. A night in a ryokan or onsen would go well with a visit to Nikko.

I know there is that saying about Nikko that all the guidebooks will translate for you, but after you've seen Kyoto and Nara, I am not so sure you really need to visit Nikko.

July will be hot and humid. The early part of July can be part of the rainy season.