Using the Shinkansen between Tokyo, Osaka and Kyoto?

You can indeed use the Japan Rail Pass to travel to both Osaka and Kyoto, the Japan Rail Pass is be valid on all JR lines throughout Japan, so if you decide to visit some other sites near Osaka and Kyoto such as Nara which contains many famous buildings such as the Tōdai-ji temple or if you wish to visit Himeji Castle your Japan Rail Pass will cover these trips as well for free. Watch out though, Himeji castle is under heavy refurbishment all through 2011, so it's possibly only worth going there if you are interested in the keep and all the defences (still pretty interesting)

You are also correct in that the NOZOMI trains cannot be travelled on.

You can plan your itinerary online using http://www.hyperdia.com/. When searching remember to select the correct search options, eg uncheck NOZOMI and only select JR train lines.

Thanks for your help - we'll give Himeji a miss I think

Just as an update, the renovations for Himeji were completed in March 2015. It looks fantastic and it is well worth visiting.
But if 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.
In Kyoto you could spend weeks there and not see everything. The three best sights though are the Kinkakuji Temple, Kiyomizudera Temple, and Fushimi Inari Shrine. Fushimi is the most time consuming; you could spend a couple of hours to over half a day if you want to romp over all the trails.

The Fushimi Inari Shrine is something people of all ages would love very much. And the Otagi Nenbutsuji is one of the most humorous and whimsical places you could visit in Japan - well worth visiting, even for kids.
In Tokyo a few of the best places to see are the Tsukiji Fish Market, plus the site that every last tourist goes to see, the Sensoji Temple. If you are in Tokyo on a Sunday afternoon, be sure to go visit Harajuku to see the youth with their wild fashions. Meiji Shrine and Yoyogi Park are next to it and well worth seeing also. And be sure not to miss the Shibuya Hachiko intersection especially on a weekend when it looks like half the city is crossing the street at once.