This used to drive me nuts when I lived in NYC. I took cabs often b/c I lived in Murray Hill and I took a strollercize class in Central Park (great class, by the way... terrific way to get in shape while keeping your baby with you). Anyway.... I got to be a pro at the whole taxi car seat thing. I used my snap n go, so what I'd do is put the car seat (with the baby in it) in the cab. The cab driver would usually get out to open up the trunk, so I'd quickly fold the snap n go frame and throw it in the trunk, and then buckle the car seat in by using the taxi's seat belt and thread it through the car seat. Remember to keep the car seat rear facing.
We moved out of the city when my daughter was 8 months old. Not sure what I would have done had she outgrown the infant car seat. Obviously, one is not going to schlep a Britax Marathon or other big seat around manhattan.
Check out the website www.thecarseatlady.com for tips about car seats and what to do in a cab.
Good luck and congratulations!