If you only have one day in Dubrovnik, I would suggest spending it on the City Wall Walk. It may be the highlight of your visit. It's a 2 km walk around the city with dramatic views of the coast and famous tiled rooftops. The wall was constructed between the 12th-17th centuries and surrounds the entire perimeter of Old Town. The walk can get crowded during the day, so try going early. We went when it opened, which was 8 am.