With a 1 and 4 year old, Park Hyatt Tokyo is a no-brainer. There's a neat playground literally right across the street from the hotel that they'll love.

There's also a babysitting service at the PHT, in case you and your wife would like to enjoy a romantic dinner.

(pedantic aside to Braindrain: the Yurikamome Line is an elevated train, not a "monorail". )