Shinjuku is basically Tokyo cranked up to 11 - and yes, there's a massive Godzilla head poking out between the buildings to prove it! This is the Tokyo you've seen in movies: neon everything, massive video screens, and enough energy to power a small country.
Fair warning: parts of Shinjuku (looking at you, Kabukicho) might not be the most kid-friendly, but it's such a huge part of understanding Tokyo that you can't really skip it. Just maybe save certain areas for when the little ones are asleep. The contrast here is wild - you've got Japan's busiest train station (good luck not getting lost), the slightly seedy entertainment district, and then somehow, in the middle of all this chaos, one of Tokyo's most peaceful parks (Shinjuku Gyoen).
Pro tip: The Godzilla head (which actually roars and breathes "steam" at certain times) is definitely worth checking out, and it's a good landmark for orienting yourself in the chaos. This is the kind of place where you could spend days exploring and still find new surprises around every corner - just keep in mind that not every corner is meant for the whole family!