Dubrovnik is one of the coolest cities around. While it is on the coast, keep in mind that beaches in the area are mostly nothing but rock. However, if it is warm enough, there are some great areas for jumping off of 10 to 40 foot cliffs on the island of Lokrum. I highly recommend going to Lokrum, as it is a national park with walking trails, swimming, a pretty good restaurant, and a 12th century monastery that the Habsburgs(sp?) converted into a summer residence. You can get a ferry there for a couple of bucks from the harbor. If you can, you will definately want to stay in the walled city. The hotel Starigrad is a great place to stay, but is very small. There are great places to eat if you like seafood, which is the specialty of Dalmation cooking. If you don't like seafood, there isn't a whole lot else out there. Pretty much all of the cafe type places in the city are identical, with nearly identical menus and service.
The fortress Lovrijenac is also a must see, it was the primary defense of the city for centuries and has a commanding view of the coastline and the city.
Have fun over there, it's a great town