If you are interested in the city of Dubrovnik itself, I think visiting it in October is a good idea. Certainly much better than in summer when it is horribly crowded and more expensive.
I’ve never sailed over there myself, but if you are thinking of renting a yacht for a week or so I think you would have a good chance of some good winds, while it could be still warm enough for swimming. In such case I would certainly plan visiting the island of Mljet. Try googling for images with keywords ‘Mljet national park’ and you’ll see why. I have sailed to islands of Lastovo and Kor?ula which are next north east and it has been very nice. As far as weather can be predicted and generalized, this area should have better weather than the northern part of the Adriatic sea. But the middle is good too, and since it’s more packed with small islands, might be an interesting alternative if the city of Dubrovnik is not your prime reason for landing there.
If you had dinghy cruising on your mind, than in my opinion there are better options… If you want me to investigate something a bit more for you, just let me know here or by PM/email.
The short video featuring Ralph is moved to youtube as google decided to close down the previous service.