There isn't a shortage of pools or beaches to swim in Dubrovnik. But when you want to get away from the crowds in the Old Town, take a day trip to the close by Lokrum Island.
The boat ride takes about 15 minutes and it costs less than $7. The more reason to go. The island is very peaceful, with no cars and the only inhabitant being peacocks, it is the perfect place to walk around and explore.
Be sure to go to the Dead Sea Pool- a unique lake linked with the sea with very calm waters, it is the best to swim in! Just be careful not to slip on the rocks as I did if you were planning not to get wet. Although, once you're there, it'll be very hard to resist swimming in it.