The original Pizzeria Uno and Pizzeria Due are two blocks north of there and open late. Especially with a baby, phone ahead with your pizza order to avoid waiting 30-45 minutes while seated for your pizza to bake.
When I had visitors with small children visiting, I went to Grand Lux Cafe, which is right near there, and it worked out fine. It's a chain, but it was a good choice under the circumstances.
Sayat Nova serves Armenian food near there and is open somewhat late.
A lot of the other places open late are bar type places and might not be the best with a baby - places like Quartino, Pops for Champagne, Rockit Bar & Grill, etc. There are also steak and seafood type restaurants that might or might not be the best - David Burke's, Shaw's Crab House, Joe's Seafood and Steaks, etc.
For a huge menu of very good to great food Grand Lux is perfect with a baby. We go there all the time with little kids. It's a half-step up sister restaurant to Cheesecake. Just like Cheesecake, nothing is spectacular, but always good-- the Southwestern and Manhattan salads are my favorites along with their warm sourdough bread. The fresh baked chocolate chip cookies are very good AND the most fattening and of course delicious item is the Grand Lux Melt. If you like a really good burger with gooey cheese on crusty bread that you kinda need to eat with a fork and knife, you'll be very happy.
Oysy sushi is right there too and they are totally kid friendly if you bring baby's own food.