I found that having a sling that the baby could snooze in allowed me to just go about
my day a little more normally. Infants are just little lumps for a while--adorable lumps,
don't get me wrong, but lumps nonetheless! Taking walks is also good. When they're
so tiny, you can do almost anything with them and it doesn't really matter, so long as
you're comfortable (if you're nursing or you can get around easily transportation-wise).
My son is now almost 4 months old and he enjoys trips to the grocery store, etc., just
because he can be looking at new things and faced. Keep talking to your baby too-I
feel silly sometimes asking my son what he thinks we should have for dinner, but
it keeps you engaged with your kid. It's a little easier when they're a little bigger. My
son will smile at me when I chat with him while we're out, so it's good reinforcement
for me to keep doing it.
There's also something called the Lila City Guide, a book of suggestions of stores,
activities, restaurants, etc that are kid-friendly. The one for my city (Cleveland) was
sort of lame, but I'm sure the NYC version has tons of great suggestions.
Don't let yourself go nuts! The more you get your little one used to going out and
having adventures, the more likely it is that they'll be open to it later!
Good luck!