I'm tempted to say Go west young man.

But I would suggest staying more than a weekend in any place. Getting off the plane after a long flight to, say, NRT and then trying to get a sense of the place is going to be an exercise in frustration imho.

I understand the plan -- I guess I just don't think it makes sense, though your mileage, as always may vary. Look for a place with cheap fares and off you go, for a few days!