The JR Rail Pass will allow you to take the Narita Express train to and from the airport, the Shinkansen between Tokyo and Osaka and any form of transportation on the JR network (including trains between Osaka and Kyoto). The break even point for the cost of the 7 day rail pass is usually satisfied with the round trip ticket between Tokyo and Japan so it makes sense if you’re going to use the pass within those 7 days.

Couple of caveats however... the pass doesn’t cover the Nozomi trains on the Shinkansen, which is the fastest train between Tokyo and Osaka. You can take the Hikari trains which are slightly slower due to extra stops. And most importantly, the validity of the pass is based on calendar days so it will expire on midnight on the 7th day. This is important because it could impact how you can use your pass depending on the length of your stay. For example, if you arrive in Tokyo in the evening and immediately activate your pass at the airport to take the NEX train to the city, you will have effectively “lost” a day because the pass will be on its 2nd day once the clock strikes midnight. Depending on your itinerary, it might be best for you to pay out of pocket for the transportation from Narita to Tokyo and activate your pass on the day that you travel to Osaka to maximize its value.

You can go to hyperdia.com to look at the train schedules and costs to help you figure out whether the JR Pass is worth your while. Just make sure to limit your search to JR trains and exclude the Nozomi Shinkansen.