When we were in Shanghai last year, we docked in the river across from Pudong where they are building a large cruise ship port. It was just a cheap taxi ride to either central Shanghai or Pudong. HOWEVER, I don't know if Royal Caribbean uses that port; the ship might be too large. This should be an easy question for your travel agent.
The Grand Hyatt is in a wonderful location; you will really love the hotel. Taxis are dirt cheap in Shanghai so you will have no problem getting to the ship wherever it is docked.