I don't know how much a taxi would cost (probably a bit, since its across town and on an island you have to get to), but by train, you need to get from the Park Hyatt to Shinjuku Station ( I think the hotel has a shuttle) take the Saikyo Line to Osaki Station, change to the Rinkai Line to Tokyo Teleport Station (about 25 minutes travel time/480yen) and walk to the hotel from there (about 10-15 minutes walk I guestimate). (Some trains on the Saikyo Line have through service right through the Rinkai line, so you might not have to change trains. A bit time consuming especially getting to and from the stations.

Alternately you can go to Shimbashi Station, change to the Yurikamome to Odaiba-kaihinkoen station, the hotel is across from that station, though the trip travel time is longer.

I'm not sure the situation, but If you need to make the trip every day, I would consider, staying at the LeMeriden Grand Pacific itself, or some other hotel closer (Hotel Nikko is across the street), the Intercontinental is near the Yurikamome line with access to Odaiba, plus various other hotels.