I will be staying in Tokyo for the first time in December. Two nights at the Park Hyatt. I will be taking a bullet train from Osaka (2 nights there, also for the first time). A few questions:

1. Which train to take from Osaka?

2. Any overview of the area around the Park Hyatt. Any absolute must things to do/see/eat for a first timer on a short stay?

3. Any favorite places to shop in the section of Tokyo with all the electronics stores?