You’ll want to have a plan for getting to & from the airport before you leave on your trip. We find that if we travel light, we can often take public transit to our hotel or apartment. When that isn’t possible, we’ve usually been successful in finding a limo or shuttle company that can provide a car seat.
We love travelling on the metro, train and busses with our kids. They love it too, and for them it is part of the adventure! Busses can be especially nice because you can see the city as you travel.
In most cities (Even in the US) a car seat is not legally required in a taxi. However, you’ll have to decide whether you are comfortable letting your child or children travel without one.
Most major cities have some sort of tourist bus that visits all the major attractions. These can be a great option as they’re fairly efficient, save you the hassle of figuring out transportation between each of your stops and because they’re usually Double Decker busses, they can be fun for kids!