1. Fly into Tokyo and fly out Osaka. This could be a cheaper option then taking train back to Tokyo from either Osaka or Kyoto. This tip could also save you time in travelling which can invaluable in Japan.
2. Kyoto is expensive especially in holiday season. Why not stay in Osaka instead. It is a much bigger city with more accommodation options and is only a 30 minute train journey away from Kyoto. Trains are always reliable and run late. If you have a Japan Rail Pass this journey will be covered and not cost anything extra.
3. Japanese public transport is the best in the world. I was in awe of how clean, efficient and reliable it is. Do not be afraid to stay somewhere slightly further away from centre because getting to places will be very easy to get to. For example, in Tokyo you do not need to stay in Shinjuku or Shibuya. As long are your accommodation is near the JR Yamanote Line then all the tourist places will be within a 15 minute train journey. The Yamanote Line is a circle line around Tokyo City and nearly all the major attractions are along this line.
4. To save money on Rail why not take busses across Japan. The major cross city bus companies have equivalent Rail passes which let you travel across the entire country on a fixed fee. These can be significantly cheaper than using the train, however, travel does take a lot longer. What you save in money you lose in time. Willer Express is probably the most popular company to use for bus travel.
5. Drink tap water. Not only is it safe and free it is actually delicious due to the volcanic nature of the country. It is standard practice for Japanese restaurants to provide free water as soon as you sit down at a table. When ice cold it is genuinely the nicest water I have tasted, let alone tap water.