Of the answers so far, Chelsea gave the most accurate answer. That's where the babies and lovely young families are--tons of them. But others, like Mitchell Hall, gave interesting statistics that are true--1 out of 20 are babies in Manhattan. You should see them on the UWS and UES!! (All the areas Chelsea talked about) Victoria Felix has some interesting info to add about Battery Park City, too..
My suggestion is that you and your wife should yourselves, one weekend, check out the UWS (try the W. 70s and Broadway, to start. Look at all the best markets in town there (72 - 80th Sts.). The UES (Try E 86 St.(esp. the groceries at Fairway, on 86th and 2nd Ave.) and the rest of the 80s down to about 73rd St. to start.) Then try Battery Park City. It sounds interesting. I know less about it than I do the others.
New York Magazine's ratings are only if you're open to ALL the boroughs. My suggestions are if you want Manhattan.
The 10014 area is the West Village, as I'm sure you know. It's a lovely area--not big, not much housing, which all translates to expensive for what you get (just under a $ million for something small and no baby's rooms) compared to also expensive UES and UWS, which have better values for family needs--bigger apts, still expensive, many with baby's rooms. But, the West Village is mostly single, very densely populated (small apts). If you were single, I would call it ideal. If you love the West Village, though, there is no reason you and your wife couldn't get something. But when I've been there, I've seen no babies or small children. Nothing like the UWS or UES on a Saturday or Sunday.
Hope this helps.
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