The Tokyo Park Hyatt does offer free scheduled shuttle service to and from Shinjuku Station, which is the city's largest. Taxis, though pricy, are available in front of the hotel and also can be hailed on the street. As many cab drivers do not speak English, it's best to get a card from the concierge that spells out your destination -- as well as the hotel name -- in Japanese.
Although most visitors don't come to Tokyo to pore over books, we do wish the tantalizing volumes in the library weren't kept under lock and key. It would be lovely if there were a public space where guests could take a book and page through it rather than have to ask someone to unlock the cases and then shuffle back to their room with a selection.
One other issue: Why doesn't the hotel make Lost in Translation one of the selections on its movie menu? In this venue, it certainly earns a legitimate place with other films the property identifies as Classics.