In the last twenty years there has been a massive realignment of military bases from overseas to stateside. Some 350 installations overseas have been closed since the end of the Cold War, including some major base closures in the Philippines and across Germany. In that time with all that relocation, not a penny was saved. While all these bases have been moved back to the states, the military budget has increased from around 400 billion dollars a year in 1992 to 600 billion dollars a year right now. That does not count additional funding for the wars in Iraq and Afghanistan. While it seems to make sense that repositioning the military back in the states would save money, there is no evidence that it does. For one, the cost of stationing soldiers overseas isn't significantly higher then stationing them overseas. In fact some nations have historically PAID us to be in their country, including Japan, which you mention has quite a few bases. Secondly positioning more soldiers in the states makes doing their job more difficult and more expensive by forcing soldiers to travel further and be in less optimal position to respond when called upon.
Strategically there's a reason why we need bases spread out in other places outside the US if we want to maintain the ability to respond to crisis around the world. The first is resupply and refueling. Ships need ports of harbor, planes need refueling. One of the reason the US maintains a presence in Spain, for instance, is because it provides a harbor at the entrance of the Mediterranean and additionally a place for planes to resupply and refuel. Spain allows the US to fly its planes through it's airspace without first getting permission. So if we need to get all of our troops massed in the states (as they are more and more) out of the states to some hotspot, then that flight from South Carolina to northern Africa is going to need a place to stop and refuel and a country willing to let them through. Having existing arrangements with governments and existing facilities to handle that is important. Also troops stationed in Italy or Germany can more quickly be deployed to the Middle East then troops stationed in Kansas. Finally many more bases are located in more prosperous nations like Germany or Japan because it is easier on the families and the servicemembers who have to relocate there. While the morale of our troops might not seem all that important from a fiscal standpoint, it encourages skilled servicemembers to stay in the military and increases the overall effectiveness of those servicemembers. For instance when Reagan took office he actually cut military spending from the level it was at under Carter, but put more emphasis on quality of living, increasing the effectiveness of our military that was suffering at the end of Vietnam.