How many days in Osaka, Kyoto and Tokyo and any advice?

My boyfriend and I will be arriving at Tokyo Narita Airport on March 28th and departing from Tokyo on April 8th. We plan to visit Kyoto, Osaka, Nara, and Tokyo. We’re most excited about exploring Tokyo, so we’d like to save it for last. I have a strong interest in historical landmarks, while my boyfriend is fascinated by technological attractions, and we both enjoy visiting must see places (even the most touristic ones!) and unique and unconventional sights.

With 11-12 days to explore, how should we divide our time among these destinations? And what would be the best order to visit these cities? Any tips or suggestions for making the most of our trip would be greatly appreciated. Thank you so much!