Just to make it clear. The Park Hyatt Tokyo is in Shinjuku, which is in the northern fringe of Tokyo. I think the hotel is excellent, but not the location. Shinjuku is a prime commuter area, the traffic to/from downtown could be horrendour during rush hours.

Hilton Tokyo is only a few blocks away from Park Hyatt Tokyo. Neither is in downtown Tokyo. There are no Hilton or Hyatt in downtown Tokyo. Downtown hotels are mostly Japanese. Westin, Holiday Inn, Intercontinental are chain hotels with properties near downtown Tokyo.

BTW, Tokyo is a VERY big city. I consider the areas around Imperial Palace, Tokyo station, and Ginza (shopping area) as downtown.