RE: NYC with newborn
We took Sarah to Manhattan when she was 8 weeks old. I wouldn't take a baby to the theater, but I wouldn't think twice about bringing one to ANY museum. I actually find museums to be good places to nurse, they always have hidden benches, nooks and crannies, and small, unvisited side rooms.
As for restaurants, again, depending on her personality, I wouldn't have any qualms. If she is really fussy or colicky, then maybe not, but of she is generally contented in the evenings, then sure!
HTH,
Beth, mom to older DD (8/01) and younger DD (10/06) and always missing Leah (4/22 - 5/1/05)