Hi,
Given that you have almost 7 full days, you are trying to see a lot of the country. You can cover many of the best places though, and a 7 day pass would work out perfectly, activated from Narita Airport for the Narita Express and able to take you by JR trains to Kyoto/Osaka and back to Narita.
As a suggested itinerary, you might try this:
Day 1 - See Tokyo
Day 2 - Day trip to Nikko
Day 3 - Go visit Kyoto til early afternoon, then spend half day in Nara Park
Day 4 - See Kyoto til early afternoon, then see Himeji Castle/Kokoen Gardens
Day 5 - See Kyoto during the day; see Osaka from the evening
Day 6 - Return and see Tokyo
Day 7 - See Tokyo if any time open; go back to Narita
The above is pretty packed but doable if you don't linger. The big 3 places in Kyoto are the Kinkakuji Temple, Kiyomizudera Temple, and the Fushimi Inari Shrine which is something people of all ages would love very much. There are also numerous places around all 3 of those to fill up your time. In Nara the area around Nara Park is the best with the Todaiji Great Buddha, deer feeding, Kofukuji Temple, Kasuga Shrine, and Isuien and Yoshikien Gardens. It takes very little time to get from one to the other.
Osaka is largely a clone of Tokyo but after the temples of Kyoto close down around 5 PM, 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 terrific.
Himeji has Japan's finest castle and it's one of the originals - not a reconstruction. The many gardens next to it are also a delight for the senses and largely skipped by the tourist masses so they are not crowded. Nikko north of Tokyo is also a real gem of a place and not to be missed.
