Dubrovnik is on the southern part of the Croatian coast, and is a very popular tourist spot. We went in October, 2009. While it was past the peak tourist season, there were still plenty of people coming in busses and off cruise ships.
The best known part of Dubrovnik is Old Town (Stari Grad), surrounded by thick, stone walls. Within those walls are narrow, cobblestone streets and lots of stairs on the north/south streets. Even though the city was heavily damaged in the 1991 war during whch Croatia separated from Yugoslavia, it was repaired with great speed.
We stayed in a soba, a room in a private home. Ours was located at the eastern part of the city, near St. John Fort (Trđava sv. Ivana).
You can walk along the top of the Town Walls (Gradske Zidine) and it gives you great views of the city.
The main street going through Old Town is The Stradun (Placa).