Best place to in Tokyo: Akasaka, Shibuya or Shinjuku?

Me and my 13 year old son are planning to go to Tokyo later this year and these three places seem to come up a lot as recommendations for when staying in Tokyo - Akasaka, Shibuya or Shinjuku. If there are other areas that are better, I'd be happy to hear about them :)

We aren't looking for nightlife or a ton of shopping (though some shopping would be good) mostly areas that have good transit options and a fair amount of restaurants.