Are these the right fares I should be using?
In your simulation, the total of the JR fees should be 30,150 yen, not 29,590 yen.
Note : A Japan Rail Pass cannot be processed by a gate machine; you have to show your JRP to a JR attendant every time when you pass through a JR ticket gate with that pass. : A JRP traveler is not allowed to take Shinkansen Mizuho or Nozomi trains.
staying in Kyoto 9/21-9/24 and Tokyo from 9/24-9/27.
When will you fly out from NRT, on September 27 or September 28?
The 22nd of September 2016 will be a public holiday in Japan; some popular tourist spots (e.g. Himeji Castle) may be crowded with visitors on that day.
Are there any other cost saving options?
You can choose overnight highway bus to get from Kyoto City to the urban part of Tokyo; its amenity may not be enough good for a young couple, though.
Depending on where you stay in Tokyo, lower-cost options may be practical for you to get to NRT.
If you visit Himeji on the 23rd and fly out on the 27th, you can pay the JR basic fare for the route Himeji -- Tokyo -- Narita Airport; this basic-fare ticket is good for 5 consecutive days.
Sep. 21 | 22, Kyoto -- Nara, basic fare, 710 yen, 1 day. Sep. 21 | 22, Nara -- Osaka, basic fare, 800 yen, 1 day. Sep. 21 | 22, Osaka -- Kyoto, basic fare, 560 yen, 1 day. Sep. 22 | 21, Kyoto -- Osaka, basic fare, 560 yen, 1 day. Sep. 22 | 21, Osaka -- Kyoto, basic fare, 560 yen, 1 day. Sep. 23, Kyoto -- Himeji, basic fare, 2270 yen, 1 day. Sep. 23, Kyoto -- Himeji, surcharge, 3000 yen, Shinkansen Hikari. Sep. 23 to 27, Himeji -- Kyoto -- Shinagawa or Tokyo -- Airport Terminal 2 or Narita Airport, basic fare, 10480 yen, 5 days. Sep. 23, Himeji -- Kyoto, surcharge, 3000 yen, Shinkansen Hikari. Sep. 24, Kyoto -- Shinagawa or Tokyo, surcharge, 5390 yen, Shinkansen Hikari. Sep. 27, Shinagawa or Tokyo -- Airport Terminal 2 or Narita Airport, surcharge, 1700 yen, Narita Express. Total of the JR fees for the above-mentioned routes: 29030 yen.
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