We did except for in NYC - we walked most of the time we were there but took a couple of cab rides without a car seat when we hailed one on the side of the road at the last minute. Not ideal obviously, I was pretty anxious but it was fine. By that stage we'd already taken DS on the hop on hop off buses all over the city without a car seat.
There is no way we could have transported a car seat with us - the flights would have been fine - it was the rest of the time it wouldn't have possible. Three suitcases, hand luggage, baby bag, pram and of course the baby was more than enough to cart!