Unless you know well in advance a short and easy route, you may need more than 20 minutes to walk from an exit on the ground of subway Nihombashi Station to a Keiyo Underground platform on the 4th basement of Tokyo Station of JR.
The above-mentioned Google Map route is to around Marunouchi Central Entrance on the ground. (And, 1.3 km in 16 minutes sounds rather a fast pace for a first-time visitor to walk.)
If you dare have to walk to Tokyo Station on your way to Tokyo Disney Resort, you had better walk first for about 800 meters
from Exit B0 (equipped with an elevator, located near the coordinates 35.681793, 139.773026) of subway Nihombashi Station
to Yaesu South Entrance (located near the coordinates 35.678679, 139.767784) of Tokyo Station of JR.
http://www.tokyometro.jp/station/nihombashi/yardmap/images/yardmap.gifhttp://www.jreast.co.jp/e/stations/e1039.htmlThen, you can pass through Yaesu South Gate (not a Shinkansen gate), follow signs for Keiyo Line, proceed on a long, long pathway (equipped with three moving walkways) and get down to the platform for Keiyo Underground Tracks 3 and 4 on the 4th basement.
You may need about 10 minutes to get from Yaesu South Gate to the Keiyo Underground platform.
(I have made a transfer to/from Keiyo Line in Tokyo Station many times, and it requires about 5 minutes even for me to just get through the pathway, not including time in getting to lower levels.)
If you just hope to travel from subway Nihombashi Station to Tokyo Disney Resort, you never have to visit Tokyo Station of JR.
Walking distance is much shorter on the following route.
Regular fares: 390 yen.
Traveling time: about 30 minutes to South Exit of Maihama Station, about 10 to 15 minutes to the JR platform of Hatchobori Station.
Nihombashi (T-10): Track 3
| [Tokyo Metro Tozai Line]
Track 3: (T-11) Kayabacho: the end of the platform in your trainfs direction
http://www.tokyometro.jp/station/kayabacho/yardmap/images/yardmap.gifKayabacho (H-12): Track 1
| [Tokyo Metro Hibiya Line]
Track 1: (H-11) Hatchobori: the exit in your trainfs direction
http://www.tokyometro.jp/station/hatchobori/yardmap/images/yardmap.gif--Transfer via a short pathway--
Entrance: Hatchobori: via elevator, the platform on the lower level, Track 1
| [Tokyo Metro Hibiya Line]
Track 1: Maihama: South Exit.