Bus if it is direct. Train involves changing to the Metro.

You most cost effective way with four people is to use the Suica/NEX to Tokyo Station and then taxi to your hotel. You didn't say how old the kids are but if they need full priced tickets then it's probably easiest to use the NEX and a taxi.

my kids are 7 & 6 years old. Do you know how much the taxi will cost from Tokyo station to Roppongi Icchome?

During the daytime: approx. 1,600 yen

Late at night ( after 10pm ): 1,900 yen

Source: http://tinyurl.com/68tm83

S = Tokyo Station, G = Roppongi Itchome

The fare may vary depending on the traffic.

Suica and NEX:

www.jreast.co.jp/e/suica-nex/index.html

How to use suica:

http://www.japan-guide.com/e/e2359_002.html

You can top up the credit in increments of 1k yen and more via the ticket machine.

Which exit should I use at Tokyo Station to catch a taxi to Roppongi? Is there a taxi stand to wait for a taxi, or you can just stop a passing taxi?

Tokyo Station map: http://www.jreast.co.jp/e/stations/e1039.html

Narita Express arrives on the Sobu Line platform #1 on the basement 5th. Then go up to the ground level via escalator or lift, and exit from the Marunouchi Central or North Gate. You'll soon spot the taxi rank.

Thanks Optimistk, your map & direction is very helpful. I think I'll do as suggested in here. Nex + taxi. BTW, which part of Tokyo station can I find the Character Street?

The Character stores are on the Yaesu Side (opposite the Marunouchi exit) in the underground, I believe.