Dubrovnik has a superb bus service; buses run frequently and generally on time. The key tourist routes run until after 2am in summer, so if you’re staying in Lapad, there’s no need to rush home. The fare is 15KN if you buy from the driver and 12KN if you buy a ticket at a tisak (newsstand). Timetables are available at www.libertasdubrovnik.hr.
To get to the old town from the bus station, take buses 1a, 1b, 3 or 8. To get to Lapad, take bus 7.
From the bus stop at Pile Gate, take bus 4, 5, 6 or 9 to get to Lapad.
The entire old town is a pedestrian area, public transport is good and parking is expensive, so you're better off not hiring a car until you're ready to leave the city. All of the street parking surrounding the old town is metered from May to October (40KN per hour). Further out it drops to 20KN or 10KN per hour.
It's a short walk down from the covered Ilijina Glavica Car Park to the old town, but a hard slog back up. Note that the daily and weekly rates are for prepay only; the machines don't make this clear and we've witnessed people being stung with hefty bills as a result.
All of the usual hire-car companies are represented at the airport and most also have city branches.