Local Delivery- prices based on Zip Code or City?

Not city, but Table Rates can do it by Zip code, country and state.

https://www.woothemes.com/products/table-rate-shipping/

For Local Delivery or only for shipped items? Sorry, this is still not clear to me. Just making sure.

Some zip codes are further away and thus need to have a higher delivery fee..

Thanks!

You could use table rate for all – just rename the rate to ‘local delivery’. Should work the same way.

Thanks!