My pay stub shows that I paid local county taxes, but they are not listed on my W-2. Should I put them on my tax returns?

Yes, you should as this is a deduction it you are able to itemize.

It can be entered as follows:

Go to Deductions and Credits (under Federal Taxes), then scroll down to:

Estimates and Other Taxed Paid

Other Income Taxes and click state, to to section towards bottom titled, Withholding not entered on a W-2 or 1099, and enter the local taxes paid.