I was in the same place last year, did not know to take an organised tour or go on my own. In the end I went on my own way to Tokyo (3 nights), Kyoto (4 nights), and Osaka (3 nights). I felt like on my own I would be able to go at my own pace and really choose what I wanted see, I had a special interest in the Sengoku Jidai (Waring States period). I took only two group day tours for the "highlights of Kyoto" and "Himeji castle", mainly for the transportation. The rest of the sights I was able to do on my own with little difficulty, I'm pretty adventurous though.
I found Japan to be easier to navigate then I originally expected, even If I did not know much of the language (just basics). It was a breeze to get around using the bullet train to travel between cities. Once you get out of Tokyo things are generally much less expensive. My favorite city was Kyoto followed by Osaka, last place was Tokyo which for me was ok.
In the end, It was a great trip, everything went smoothly and the Japanese people were warm and friendly. Definitely brush up on some basic Japanese polite words and cultural norms/customs, you'll be bowing a lot 😉.
In Tokyo I liked:
Sensō-ji Buddhist temple
Kabuki performance at Kabuki-za theater in Tokyo's Ginza district
Samurai sword exhibition at the Tokyo National Museum
Egg salad sandwiches at Lawson Markets
Ekiben bento lunch on the Shinkansen bullet train to Kyoto
In Kyoto (my favorite of the three citites) I liked:
Tōfuku-ji Temple, great for Autumn leaves/colours
Rengeoin Sanjusangendo, home to 1001 Buddha statues
Kyoto Marui Market, incredible luxury food market at the bottom floor
Nara, the old capital of Japan before Kyoto
Kyoto International Manga Museum
Conveyor Belt Sushi at Osaka Station
Toro Tuna Tasting
Hope this helps! :)