In most cities you can easily drive a stroller onboard local trains and metros, and you are typically allowed to do so. If the stations has elevators or escalators varies wildly from city to city.
Buses and trams are different, and there you'll typically find that if the buses/trams are modern strollers work well, and there are often an area for strollers although you will need to be two persons to carry the stroller up and down.
Commuter trains are usually not stroller friendly.
In the cases of non-stroller friendly transportation a car seat works for longer journeys, but for the typical 10-20 minute journey of local transportation you'll probably find that a baby carrier is more practical.
Because of this, your strategy will be different in different cities. In Paris you would typically have to carry the stroller up and down stairs to take the Metro, while all buses have stroller-parking (that is often full, though), so for a family with a baby or a toddler a bus is definitely easier. In Stockholm both buses and subway is extremely family friendly, partly because of an almost obsessive handicap-friendliness. In Krakow we find that it's easiest to walk. I remember both local trains and buses in Chicago as being stroller friendly even if we didn't have a stroller with us, but I do not remember if there was escalators or elevators everywhere.