...as for jet lag, melatonin is the answer. Take one before you want to sleep for a few hours - whether on the plane, or at bedtime when you've arrived. I do long-haul 10-12 times a year and never travel without it.
Only been there once, but if you don't like the hustle and bustle of NYC you may not like parts of Tokyo - worse if anything. Long way to go for a week too, especially with an extended flight time (with a change), and expensive. Sorry, sounding a bit negative but I wouldn't do a trip like that...