Do you really need to spend another day/night in Tokyo before you fly home? I would do what you're going to do in Tokyo, then go to Kyoto and then take the train from there to Narita (if it's not possible, as already suggested, to fly out of Osaka <KIX>). Getting from Kyoto to Narita on the train would take about four hours, so if you leave before lunch you should be able to make it to Narita for an 18.05 flight.

A 7 day Japan Rail Pass (¥29,110) would be worthwhile as it would be marginally cheaper than individual tickets (Tokyo - Kyoto = ¥13,800 + Kyoto - Narita = ¥16,780). Any additional usage you get from the pass would be a bonus. The only downside to a JR Pass is that you can't use the Nozomi Shinkansen (the most frequent and fastest) and have to use the Hikari Shinkansen (usually two per hour Tokyo - Kyoto). They're a bit slower but only because they make a few more stops, not because the train goes any slower. If you're not already familiar with it, use HyperDia for everything you ever wanted to know about train times, fares, track numbers and generally how to get from A to B (and if you need any help figuring out how to use it, please just ask).

You should also get IC (Suica) cards. These are prepaid transit cards that can be used to pay for trains (but not the seat fee), buses, subways and can also be used at convenience stores (7-Eleven, Family Mart, Lawson). Much, much easier than getting a ticket every time you want to hop on a train or the subway. There are a number of regional variations (Suica, Pasmo, Icoca, Nimoco etc.) but they operate interchangeably throughout Japan (more or less). Suica is issued by JR East in Tokyo, Pasmo by the non-JR private railways/subways in Tokyo - I'd get a Suica. If you have iPhones (8, X, XR, XS), you can load a virtual Suica card in Apple Wallet and top it up using Apple Pay - very convenient. If you get a physical card, it can be topped up at ticket machines (but cash only).
https://www.japan-guide.com/e/e2359_003.html