Tokyo - Osaka - Kyoto - Tokyo

Hi there!

I do think that a 7 day JR Pass would benefit your travel, given that you make the return Tokyo - Kyoto/Osaka within 7 days. The return is about the same price as normal JR tickets and you would already be making savings if you use it to travel to and from the airport as well.

You can exchange the JR Pass at Narita Airport between 6:30 - 21:45 (the desk may vary depending on the time of day). You can use Hyperdia.com to look up time tables and other route information, I already looked up the route for you here. The last train going to Kyoto from Narita airport leaves at 18.19, so you should have enough time to catch a train to Kyoto on the day of arrival.

As for how to travel I would go Narita Airport - Kyoto - Osaka - Hakone - Tokyo. You can use the JR Pass to travel to Odawara the Shinkansen station for Hakone, from here private railways run into the area and a Hakone Free Pass can be a good supplement to your JR Pass.
You can either book a seat in advance or just hop on the train as you like, the JR Pass allows for both.

I hope this helps!
Daniel