First, a space elevator would lower costs of getting getting things into space to a fraction of what it is today. If they allowed tourists, you could afford to go. It might get as low as a few hundred dollars (long run, not short run, obviously). At first you wouldn't actually be able to go because tons of technology companies would be working like mad to take advantage of this and they'll all be lined up in front of you. The micro-gravity in Earth orbit would be a huge boon to many areas. There could truly be a technological revolution here, not to mention an explosion of business in space.
So who cares if the Japanese build it first? Well, the US should, for one thing. The Japanese price tag of $5 billion is a joke. It will cost them far, far more than that. However, the real cost of building a space elevator is actually the cost of building the first space elevator. If you have the first one, subsequent ones are actually cheap. Not only do you have the technology, you then have the access to space. All of my reading of space elevator technology suggests whichever country or group first builds a space elevator will have such a dominant position in the industry that it will be very difficult for any others to overcome. If the US then tries to put up an elevator, the Japanese can just put up two or three more for a pittance, further increasing their dominance in space.
So if Japan succeeds, the US, like every other country on the planet, automatically becomes a second-rate player. The Japanese will be the ones who could potentially solve our energy crisis. The Japanese will be the ones who be able to chase down rare materials we can't get on earth. The Japanese are the ones who will make huge strides in materials technology. And even though they have almost nothing by way of a military, they stand to become a hugely influential military power ("Oh yeah, we'll just take out all of your satellites!").
Frankly, I won't be too disappointed by this. I want someone to take advantage of this. Better the Japanese than no one.