By foot from Dubrovnik to Dubrovnik (city)
If you come ashore by tender boat in the old harbor, you're almost in the old town. From the tender boat station, you can already see the big entrance gate.
If you dock at the new harbor at Port Gruz it's also possible to walk to the walled historic city. It will take about 20 minutes. From the pier, walk toward the marina, at the end of the dock. From there, the historical town is well indicated.