We're the rare New Yorkers with a car (we travel a lot and our neighborhood has great on street parking)! We used the Chicco keyfit bucket seat for the first 14 months or so (our son was/is a little guy), and it was really easy to get in and out of various cars using the base system. I used it several times by myself (I don't actually have a license either so I don't drive our car) if I had to use a car service to get to the airport etc, since my parents have a car seat for him to ride in on the other end. There are several car services in the city that provide car seats for a nominal fee, usually graco or cosco brand seats, and you can request a convertible or an infant seat with a base usually. Especially now that he uses a convertible seat, I make a request that it's rear-facing and ask them to come a little early so that I check that it's properly installed, although there have been a few times when it's been front facing and I just let it go.
As an addendum to grizzle's original question about car seats, can all convertible seats be used for infants? I thought that I remembered some people on carseats.org saying that there were some that shouldn't be used before 6 months or some height/weight minimums, but I didn't pay much attention since we were way beyond that.
Do you have any friends with cars and babies? Maybe you could ask them to pick you up at the hospital...I know we've done this a few times for friends with our infant seat.