Originally Posted by
Pickles
There is the Conrad in Shiodome.
My thought as well. Then in the morning, taxi or Yamanote line to Tokyo station and take the Narita Express to the airport.
OP: Note that you should almost certainly leave your hotel at least 3 hours before your flight, given that you don't know your way around. Work out the train schedule with the hotel when you check in; ideally you should even buy your ticket the night before.
And I wouldn't expect to see much of Tokyo with that layover timing.