OK, so it is six nights in Tokyo, that makes sense. Here is what I suggest:
21st: Arrive. Get N'EX + Suica deal to get to Tokyo. The N'EX ticket will get you to any JR station in Tokyo. If you have to use the subway, the Suica will get you there.
22nd: Tokyo
23rd: It's Sunday, it has to be Yoyogi Park/Harajuku.
24th: Kamakura. I would suggest the Kamakura Enoshima Free Kippu:
http://www.japan-guide.com/e/e2358_004.html25th: Tokyo
26th: Nikko
27th: From Tokyo to Toyohashi, drop luggage and then go to Himeji (possiblely arriving around 14.00). Evening, continue on to Hiroshima and stay overnight.
28th: Hiroshima/Miyajima. Evening return to Toyohashi
29th: Nara
30th: Osaka
31st: Kyoto: Consider another overnight stay.
1st: Kyoto
2nd: Nagoya (Luggage in locker at Nagoya?). Evening, train to Tokyo.
3rd Keisai Airport Express to Narita, 1,000 Yen.
I've not put in train times because they will change on March 15th. You can work out your timings here nearer the date:
http://www.hyperdia.com/cgi-english/hyperWeb.cgiI think you really have to do the overnight in Hiroshima. Toyoko Inn have good prices, 6,090-6,300 Yen for a single in Hiroshima:
http://www.toyoko-inn.com/eng/As you are arriving late, I would go for the Hiroshima-eki Shin-kansen-guchi location that is 3 minutes from the station @ 6,300 Yen. There are currently plenty of rooms available.
The Kyoto Shijo-Karasuma location still has singles (smoking only) left for the 31st @ 6,720 Yen. These will go fast, so if you think you would go with this make a reservation on-line now. You can always cancel up until the day of arrival.
I think that covers most things, any questions?