We plan on leaving Toyko (will be in the Narita area) on 19 April and will travel to Hakone. We would like to spend two nights in Hakone and are planning to overnight at the Prince Hakone Hotel.On the assumption you'll use the 7 day Japan Railpass, I'd give you detailed info.
From Tokyo to Odawara, take the Shinkansen Kodama or Hikari. The former runs every 30 minutes, the latter runs every 2 hours and both take 38 minutes.
There is a complimentary courtesy bus service for the Prince Hotel customers between Odawara Station and the hotel.
The hotel-bound bus leaves Odawara Station West Exit at 11:30, 14:00, 16:00 and 18:00. Advanced booking is mandatory. Contact them over the phone:
+81(0)460-83-1111
Bus stop map
http://www.princehotels.co.jp/hakone/bus-info/index.htmlYou might use skype if calling internationally. It's amazingly cheap.
Hotel to Odawara (Booking between 3pm the previous day and 30 minutes before the departure.):
10:30, 13:00, 15:00 and 17:00
The Shinkansen Hikari leaves Odawara for Kyoto as follows:
Odawara 7:03--9:14 Kyoto
Odawara 8:09--10:14 Kyoto,
then it leaves every two hours the same minutes past the hour until 18:09 and takes 2 hours 5 minutes.
From Kyoto to Hiroshima, there are only three direct Hikari trains daily.
Kyoto 7:49--9:35 Hiroshima
8:02--10:01
8:22--10:25
If you travel afterwards, you need to change trains en route.
e.g. Kyoto 8:38--(limited express Raicho)--9:01 Shin-Osaka 9:11--(Shinkansen Hikari)--10:39 Hiroshima
Kyoto 9:39--(Shinkansen Kodama)--9:53 Shin-osaka 9:59--(Hikari)--11:28 Hiroshima
From Hiroshima to NRT, if you catch the first Hikari ex-Hiroshima, you'll get to NRT 2 hours before the scheduled departure time of your flight. Usually 2 hours is plenty enough to check in for a flight at Narita from my experience, though 25th of April is the beginning of the people's exodus on the golden week. I'll leave it to you whether you leave Hiroshima on that day or the day before.
24th April
Hiroshima 18:51--(Hikari)--20:27 Shin-Osaka 20:33--(Hikari)--23:26 Tokyo
Then the following day:
Tokyo 11:03--(Narita Express)--11:59 NRT
25th April:
Hiroshima 6:22--(Hikari)--8:24 Shin-Osaka 8:40--(Hikari)--11:33 Shinagawa 11:50--(Narita Express)--12:56 NRT
Hope this helps.