If you have a 7 day JR Pass and you activate it on Apr. 12th, and depart Japan to go home on Apr 18th, taking the Narita Express train from Tokyo to Narita, then with your itinerary it would pay off. Otherwise, you would be a little short - but you could easily make up for it by taking a day trip from Tokyo to Nikko, for example, which would be well worth it.
If you can, staying an extra day in Kyoto would be worth it as well (Apr 12-14). And since you are already going to see Tokyo, you can largely skip Osaka during the day time. After you see the temples/shrines in Kyoto, which close around 5 PM, you can also go see Osaka in the evening, which is when the city becomes alive. It only takes about 30 minutes between Osaka and Kyoto by express train. Dotonbori is a great place, and the night views from the Umeda Sky Bldg and Abeno Harukas are tremendous:
https://www.youtube.com/watch?v=COJ_MeXbeow
https://www.youtube.com/watch?v=xb1wuyAGgyQ
https://www.youtube.com/watch?v=-AyUZmGbW8g
Seeing Nara is also well worth it - which still leaves you Apr. 16-18 for Tokyo and a day trip to Nikko, or Hakone, or Kamakura if you like.
By the way, for your arrival into Narita on Apr. 11th, there is a cheap 1000 yen bus you can take from Narita to Tokyo:
http://accessnarita.jp/en/home/