Split, Croatia is also great it's actually a medieval city built inside a Roman palace: http://flickr.com/photos/pelle/sets/72157604400174148/

Close by is the island of Hvar, which is also pretty amazing. It was built by the Venetians as a trading outpost: http://flickr.com/photos/pelle/sets/72157604497939272/

A great resource for someone wanting to learn about how these kinds of places help mold our modern business world, I recommend Nick Szabo's blog Unenumerated. See this post about Genoa for example:

http://unenumerated.blogspot.com/2006/10/genoa.html

+1. This would be the best time to visit Dubrovnik because there won't be as many tourists as in summer.