I need recommendations on things to do and places/neighborhoods to stay in Japan for 3 days.

I will be arriving in early July into HND and flying 3 days later out of NRT.

I'm mostly a Starwood traveler, so any recommendations for hotels within the chain help, but I'm open overall to good neighborhoods to stay at and even if it makes sense to try to visit other cities during my short stay, such as Kobe or Kyoto... (I will be flying from SIN, so jet lag shouldn't be an issue... hopefully)

Thanks,

Mike