Many of the best pizza places aren't terribly child friendly. They're often either hard to get to (Di Fara, Patsy's, Spumoni Gardens), or tiny holes in the wall without seating. And I'm not sure you're going to find anything in walking distance of Times Square that comes close to "best" pizza (although Pizza Suprema is indeed pretty good, is not too long a walk, and I believe they have seating).
For deli, Katz's is indeed probably the most classic (think "I'll have what she's having" in When Harry Met Sally). And it's very close to a couple of playgrounds for burning off four year old steam if the weather isn't too bad (there's one at First and First right across Houston and another at Norfolk and Houston--enter on Norfolk).
For stuff to do with a 4yo, my 4yo LOVES ToysRUs in Times Square. And not because he wants to buy stuff (we have him pretty well trained that you go to TRU for the ferris wheel, the giant dinosaur, the train displays, etc.--not to actually buy toys). And it's just a couple blocks from your hotel. It's way better than FAO Schwartz these days (sadly).
A lot of kids will enjoy a pedicab or (if you don't have an issue with the treatment of the animals or the price) horse and carriage ride in Central Park. Or you can rent a bike with a kids' seat and explore Central Park yourself. There's also a decent zoo in Central Park--don't miss the penguins.
Other stuff that's walkable:
- Playgrounds: Most aren't all that special, but if you're traveling with a 4yo, you'll want a place to blow off steam. I think the closest to your hotel is along 10th Ave between 47th and 48th. There are also great tacos across the street in the back of a bodega called Tehuitzingo.
- Escalators: If the weather is bad, you can go to the mall in the Time Warner Center at Columbus Circle and ride the escalators up and down, which usually are pretty empty on the 3rd floor (again, nothing special, but something physical for a 4yo to do). Landmarc in the Time Warner Center is also a good place to go for a nicer meal out with kids--it's one of the few restaurants in the city where the ratio of wine bottles to kids at many tables is roughly even.
- The Top of the Rock observation deck is also great. Much better with kids (or anyone for that matter) than the Empire State Building, because the tickets are timed so the lines aren't obnoxious and you get great views of the Empire State Building and Central Park.
- Sixth Ave: Kids will be impressed by the fountains and tall buildings along Sixth Ave in the 40s/50s. And there are big plazas where they can run around. And food trucks for a bite.
And of course Natural History and the Children's Museum on the UWS are great.