If you are really on a budget, take one of those 5000yen overnight buses from Tokyo to Kyoto.

For trains:
There are some discount tickets that you can purchase.
In specific for Tokyo-Kyoto you can purchase a discount Kodama Shinkansen Ticket (has to be purchased at least one day in advanced at special JR Tours offices located in Shinagawa or Tokyo Stations, as well as other locations, I find the Shinagawa Station one to be the easiest to find):
http://www.jrtours.co.jp/shop/shutoken.html
Shinagawa Station Branch:
http://www.jrtours.co.jp/shop/page/J...h.aspx?bc=E477
It's on the Shinkansen side.

The cost is 9800yen, again its on Kodama Shinkansen trains to Kyoto from Tokyo/Shinagawa Stations. The Kodama is the "slowest" of the Shinkansens, taking 1 hour longer (a 3hr 45min trip vs 2hr 45 on Hikari vs 2hr 20mins on a Nozomi). But for 9800 yen vs 13,000+ for a regular ticket, I could deal with it.

http://www.jrtours.co.jp/kodama/tokyo.html

The timetable of Kodama trains is at the bottom of that page.
東京 = Tokyo
品川 = Shinagawa
京都 = Kyoto

For Kyoto - Hiroshima, you could look into one of the Sunrise Tour plans, which includes a roundtrip ticket Kyoto-Hiroshima plus hotel for about 20,000yen, a good deal since round trip would already cost about 20,000 normal ticketing alone.
http://www.japanican.com/tours/FTour...VJNH2A&aff=EXJ