Drink Dubrovnik water - it is extraordinary, don't buy a bottled one (except in restaurants where it is defined by law). Eat mussels, they are so fresh and tasty.
Admire great views from Srđ. Eat oysters (brought from Peljesac). Visit Lokrum, spend the whole day there if you can. Drink Plavac. Visit
Dubrovnik Summer Festival in July or August. Visit Julian Rachlin & Friends festival in September. Take
Jadrolinija boat and visit at least one of Elaphiti Island. Take a bath at St. Jakov beach. Taste an ice cream
at "Dolcevita". Walk the city walls. Don't avoid dark streets and corners, they are all safe.
Try to choose an early flight for your wedding in Croatia and admire Croatian islands from the air. Take a night bath at Banje beach.
Drink more wine on Peljesac, visit cellars there. Visit Arboretum at Trsteno (15km west from Dubrovnik) - if you are a small wedding party you may get married there too, :).
Eat fresh fish for your Dubrovnik wedding dinner. Go to Peljesac and eat Oysters and Mussels in Mali
Ston. Choose to have a wedding lunch instead of a wedding dinner, so you can take a bath afterwards and party
(or chillout) in the evening. Take at least one early morning bath (7pm?). Try prsut (tasty smoked ham).
Go for at least one concert of Sorkocevic Quartet. Check out Dubrovnik's rooftops while walking the city walls.
Visit Lovrijenac (check the image in the background for unbeatable views).
(Aug 2011 update)
Take a listen of some of Teo's gigs, he sounds like this. He performs often during summer in different lineups (trumpets, drums, female vocals, cello, violin, depends on the day) always on nice terraces (e.g. Grand Villa Argentina, Argosy, Hotel Croatia Cavtat), you'll be surprised by his performance.
Rudi started this season his amazing wine tastings, so if you're fond of wines (and local gastronomy too) just go for it. Here is his Dubrovnik wine tasting site.
You're walking the Old City and it's reaaaally hot? In less then 2 minutes you may jump into sea, just go for one of two small Buza exits through the City walls. Careful on the rocks!
You're fed up with seeing people around? Take a journey to Prevlaka (peninsula, the southest peak of Croatia) - just rent a car for the whole day.
A small and tiny disclaimer: Mentioning the above places is not any kind of ad nor marketing: these are just places that we personally like to visit.
Send us some more Dubrovnik Wedding tips (we surely forgot many things).