The old town is beautiful, but can be easily absorbed in a few hours. Which, if you came only to see the town, will leave you perhaps a little disappointed. There are, however, plenty of places to swim and relax. On the main part of Dubrovnik there are no sandy beaches, just the odd bit of pebble beach in between rocky cliffs. The islands, however, offer better places to relax. Ferries operate the islands regularly. Compared to Zagreb, Dubrovnik is expensive.
Insider Tip:Don't concern yourself too much with being close to the old town. It's really not worth paying a large amount of money to be in there, especially when you'll probably see all it has to offer in a day. Also, it's quite expensive in the old town.