Another fun thing to do when visiting Dubrovnik is to head to the hills—via cable car. The Dubrovnik Cable Car whisks visitors high above the Old Town, up Srd Hill, with the views only getting better and better as you climb (on clear days, it's said you can see for some 50 kilometers).
Attractions to look out for include the 19th century Imperial Fortress, built by the French during their occupation of the region and now housing a fascinating exhibit pertaining to the Homeland War of 1991-1995, when the city was defended against hostile forces.