If you want public transit be more popular, build denser cities. E.g. on Manhattan using the subway is a no-brainer, and you are rarely more than two (long) blocks from a subway station. In some more remote parts of Brooklyn, you often cannot reach the destination by subway alone, and you have to take a bus. Even further away, traveling by a bus either becomes too slow, or the bus does not come close enough, and a car is inevitable. I suppose there is no way to make public transit economical or time-efficient in agglomerations like Houston, even though LA manages a bus network somehow.
Cycling such distances us also problematic: you either have to be pretty fit and take a shower when you arrive, or you have to have all the time in the world. Cycling within a dense city is pretty practical, though.