JR Pass for 14 or 21 days?

Hi,
Your itinerary is a bit less than 5000 yen short for a 21 day pass. But getting a 14 day pass and paying the regular fare for the rest would be quite high too - I'd suggest you add a side trip to cover the 5000 yen difference and then the 21 day pass would pay off. Since 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. Instead, on the 19th you might go see Himeji, which has Japan's finest castle. This would cover the difference for the 21 day pass, and you can get there quickly by bullet train.

Thank you very much! Your answer was quite helpful.