I was staying there a few month ago.
I took the bus - very convenient and not too time consuming. The bus returning to the airport goes around town (across the bridge close to the hotel - very quick). The bus from the airport to the hotel goes to the air terminal first.

Taxi from Tokyo Stn to the hotel was around 1000 yen. There is also a subway line (dont remember the name of the station, but is ins only one or two stations from tokyo station going south on the line which runs parallel to the train line. From the subway it is around a 5-10 min walk to the hotel.

The monorail seems to be fairly infrequent.

My recommendation is: take the bus.