It depends. If there was local tax withheld in box 19, you should enter which local tax was paid or use the dropdown menu in Box 20. It will usually be the locality you worked or lived in.
Depending on the state, you may also need to enter special abbreviations depending on what taxes you pay as determined by your school district, city, municipality, or other local mandates. This detailed information will be shown once you use the dropdown menu to choose your associated state. To access the information, click on the question mark next to Box 20 - Locality name. If you choose Ohio, for example, TurboTax will provide you with all the possible school district tax numbers, CCA codes, and RITA codes in the pop-up.