My family name is Zapolski.
Of the 469 people with this name... most of them come from north-east Poland.
As it is a border area then it's possible that your Great-Grandmother was born in a place that is no longer Poland. To understand this you should read up on Polish history... the short version at wikipedia.
Check your Great-Grandmother's Naturalization Records or Immigration Records. Then get back to us with a place name.
Do a search at: ellisisland.org
Enter only the surname. Make sure that you also try Zapolska
, which is the female form.