My job takes out local taxes for the area where I work, but no local taxes for where I live. Do I apply this without money for my local taxes even though it's not from my locality?

Depends where you live & work. In general. If you have not had any taxes withheld for the municipality where you live (lets call it municipality "A"), and if you owe them tax money based on your income, then you owe them some money. The fact that some taxes were withheld for the municipality where you work (call it municiaplity "B") is immaterial as far a "A" is concerned. So no, you don't apply the money withheld for "B" to the taxes you owe to "A." However, some areas have reciprocal agreements that allow you to apply taxes collected in one area to taxes owed in another.

It would really be helpful if you would get more specific - what "localities" are you referring to?