Upper Darby is a fictional Rhode Island town near Providence. Neither Rhode Island nor Upper Darby are really integral to the story—honestly, My Sister's Keeper could have been set in any predominantly white suburban town—but there is a slightly deeper meaning to the choice of Upper Darby as the site of this legal brouhaha.
We're told that "There's a Little Compton, but no Big Compton. There's an Upper Darby but no Lower Darby. There are all sorts of places defined in terms of something else that doesn't exist" (5.1.115). (There actually is a Little Compton that isn't a figment of Jodi's imagination—just sayin'.) So the name is important, if not so much the city itself. It's a city without its counterpart… just like Anna fears she's going to be (without her sister, not a suburb), and like the person Kate eventually becomes.