Traveling by Shinkansen is speedy, convenient, and yet pretty expensive. 

If you are not relying on JR Rail Pass, here is some hints for possible cost savings: 

If you need to travel from destination A to B via C or D; you may be able to save money by picking and chosing to travel on Shinkansen only on the longest leg and use other regional express JR trains.

There is also a possibility that buying a multuple day ticket from A to B while stopping on C and D, plus a Shinkansen ticket from A to C can save you even more money than buying piecemeal tickets. Ask your JR ticket counter agent who can plot a money saving strategy for you.

In Kyoto and Tokyo Stations there are special lines for foreign visitors with agnets who can speak English to help you with your travel plant. Lay out your entire train travel routes so that they can offer your the best price and options to travel.

Japan also has a large network of Highway Buses for inter-city travel, including passes which are often more economical than a JR rail pass.