When is the best time to activate 7-day JRail pass

Hi,
A 7 day pass for your itinerary would simply not pay off. You would need to return to Tokyo by bullet train as well and do some kind of side trip or use it to go either from or to Narita Airport by the Narita Express. You could, if you are willing, go spend a night to see Hiroshima/Miyajima. That would fill the difference and you can still return back to Tokyo by Jet Star.
Since you can't use the Pass both ways coming from or returning to Narita Airport, you might look into the 1000 yen bus. A 3 day subway pass for Tokyo might help you too.
Since you are already seeing Tokyo, you can largely skip Osaka during the day. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.
Don't miss out on Nara and Himeji also, which are close to Kyoto. They both have some of the finest places in Japan.

Best of luck.