Actually, things in Dubrovnik are really starting to quiet down by that time. Instead of 3-4 cruise ships a day, there is likely one or none. Some restaurants will be closed for the season but there will still be plenty of good options to eat. The walls, rectors house, etc are listed as being open on the 1st. If you would like to learn about Croatian wines and have some great glasses, try D'Vino wine bar. Sasha is an amazing font of information and also does wine tours.

Hope this helps