I haven't stayed at the Conrad, but I've had 4 stays with kids at the Andaz and love it every time. They're very accommodating, the size of the rooms is great, and the kids love all aspects of the hotel (the view, the pool, happy hour snacks, etc). Great room service options and plenty of shops/restaurants within the same complex. With the new station, Toranomon Hills is also now extremely easy to get around Tokyo.

edit: also, if you have kids and it's baseball season, I recommend going to a game. The stadium is a very short ride away. The english website had run out of tickets, and the unfailingly helpful concierge at the Andaz organised some for us (including going to a 7-11 to pick them up!). Another parental recommendation: if you'd like a date night, we use babysitters.jp.