It depends. Box 20 provides a brief description of the local, city, or other state tax being paid. The description may recognize a certain city, or a state tax like State Disability Insurance (SDI) payments.
Box 20 on a W-2 is usually left blank in areas where such communities don't assess any local income tax. TurboTax would only be asking you to put something in Box 20 if you had entries in boxes 18 and 19 as well.
If you had a locality tax for some reason withheld, but you don't have a local tax return filing requirement, you can just put the state initials in Box 20 of the state where the locality/city for which this withholding is associated (you would also choose this same state in the dropdown box "Associated State").
However, if you are required to file a locality/city tax return (or possibly requesting a refund for these taxes (if available)), you will want to contact the company that provided your W-2 and request this locality information.
You may want to contact your local city tax department to check if you have a local/city filing requirement. You will also be able to obtain any local/city tax return forms through your city tax department for the city where these taxes have been withheld.
Since each state and local government has it's own filing requirements. Here is a link to each state's Department of Revenue that may be of help:
https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue
