How ubiquitous are home water filtration systems in the USA?

It will depend on the state and the gusto of the home owner.

In some northern states, tap water tastes great and is perfectly healthy without a filter, so there is little chance to find one.
in Florida, water is ok health-wise, but tastes like cat pee (it is hot, so they add a lot of stuff to restrict bacterial growth). So households where people actually drink water would often have a filter; but if it's a soda-drinker family, they wouldn't bother.
in some specific places, I wouldn't touch the tap water with a ten-foot pole, filtered or not.
and so on.

Your best bet is to buy one when you arrive, they are cheap, and you can take it with you.

Aganju 28475

Source: stackoverflow.com