I live in Brooklyn in NYC and I purchased a car when we were expecting. It is impossible to take a baby on public transit to most places. Buses are not equipped for strollers. Train stations are crowded and inaccessible to strollers. It takes a lot of physical energy to move a child through public transit. Our family, friends, the doctor, babysitter, and schools are not all walking distance and not all at expensive real estate near the train. Having a vehicle is empowering for my family and most like it.
Although I'm all in favor of cars, taking just one baby on public transit isn't much different from going by yourself on public transit. The trick is a sling. Don't even buy a stroller. There are several types of slings for babies. You can use one with a padded pocket and strap, one with fancy parts, a big long strip of cloth, or even just a folded bed sheet with a knot behind your shoulder.