Since the 1950s, the Roppongi entertainment district has been synonymous with drink, debauchery and the like ... or so people tell me. That began to change when Roppongi Hills opened a decade ago, and a push was launched to transform the area's seedy image into something more cosmopolitan. Mission accomplished in my opinion, and one of the best examples of this transformation is the Tokyo Midtown complex.
Opened in 2007, this is — like the nearby Roppongi Hills — a mixed-use urban center that combines businesses, shopping, the arts and swanky high-end apartments. I recommend Midtown over Roppongi Hills and similar locations because families seemed to have been factored into the planning. Despite being in the middle of such a happening area, it is easily navigable with strollers and offers (relatively) open spaces where kids can run ahead without parents worrying about them slamming into taxis or old ladies.
Another advantage is that Roppongi is on the Oedo Line, which as every baby-buggy pusher knows is one of the only subway lines in Tokyo that has elevator access from platform to ground level at all stations — and considering how deep that line can get (surprised they didn't strike oil) it's downright crucial. The station exit is also in the basement level of Midtown for very easy access.