This is just completely wrong. Just from personal experience I can say that Tokyo, Amsterdam, Paris, and Florence are perfectly livable without a car.
How do you plan to get to Rainier?
Whether or not those cities are "better with a car" doesn't really matter here. OP was asking what "cities you can live in without a car", and you can do that in all four of those (I've done so in Seattle and San Francisco). Whether or not you love to do it doesn't change the fact that it's perfectly possible.
And Mt. Rainier? Really? Again - the question was whether or not you can live in a city without a car. Rainier is two hours outside of the city, so it's not even a part of the question.