In most big cities, usually in the main shopping areas near stations, you can find discount ticket shops ( kinker shoppu ) which sell, among other things, cheap airline and Shinkansen tickets. These shops (usually identified by a window full of handwritten signs indicating the cost of tickets to different destinations) buy up discount group tickets and sell them on individually, usually at around twenty percent cheaper than the regular prices. These are legitimate operations, but you'll need to be able to read and speak some Japanese to be sure you've got the ticket you need, and there may be some days when travel isn't allowed. With the Shinkansen tickets you can't make seat reservations at a discount shop, so you'll need to go to a JR ticket office as well to arrange these.