The Old Town is pedestrian zone. The closest bus stop is Pile.All buses from airport go at Pile bus stop, so you have to get off there.Very close to apartment is Parking place Buža, but the parking is paid. If you go from the port in new part of Dubrovnik, Gruž, you have to take bus num.1, 1A, 1B,1C,3 and get off at Pile.There is taxi station on Pile,too. There is 5 min walk from Pile till the apartment along Stradun.