Yeah, it really depends on how you want to spend your time. Odaiba is a very Americanized area -- lots of shopping malls, big expressway cutting through it. The area of West Shinjuku around the Park Hyatt is a high-rise business district. Two very different environments. For a trip alone or only with a partner it would be the PH for me without question, but with kids I would lean toward Odaiba even though it is a much less Japanese experience there overall.

I rather like Braindrain's suggestion of spending a day in Tokyo; the other end of the Yurikamome train is in Shinbashi, from which you can walk to the Imperial Palace, Ginza, Tokyo Station, Tsukiji, etc. etc.