Hi Scruggs,
the Park Hyatt is lovely. If you want to save some money, try the Century Hyatt - last time I stayed there, it was about 40% less expensive. If you can book this far in advance you will get a spectacular view of Mt Fuji if you request it. It is close to Shinjuku, and there is a shuttle bus if you feel lazy. The great advantage here is that there are well-priced eateries on the perphery of the station with a genuine Japanese feel to them, as opposed to international restaurants.
What to see? It will be winter, so I am not sure whether the park down by the harbour will be very pleasant - it could be a little cold. There is a walk you can make which takes you through the diplomatic areas - about five kms, I guess from memory - through parks and past a few beer vending machines
The trains are fast, reliable, clean, air-conditioned, and inexpensive. This is because Kne Livingstone does not live there. However, peak hours will be just that. Either get stuck in early or take it easy and avoid the mob.
Akihabhara (the electronics district) will distort your brain in a very pleasant way, and it's a must.
The only other advice I can give you is to start studying the language a bit in the run up to your trip. You will understand little of what's being said, but your endeavour to say the basics will be appreciated. Make sure you know what is considered rude there, and don't do it.
Have a safe trip and please report back!
BOFH