There's Manchester-by-the-Sea, MA. There's also a lot of "New" versions of older European locations as a way to distinguish them from other similarly named places when there aren't any rivers nearby, I guess, like New Jersey. Don't forget, a lot of places in the US were also already named before European settlers arrived.

It might also simply not be needed as a matter of practicality. There are many Springfields, but probably not very many per state (although I know New Jersey has two) and certainly a max of one per zipcode. Sure Springfield, MA 12345 isn't as whimsical as Springfield-upon-the-Connecticut (or whatever) in terms of distinguishing it from Springfield, NJ 08765, but it gets the job done.