Been a couple of times in the last few years, first time stayed in Dubrovnik, next time on one of the islands about half an hour or so from the port, Lopud.
There's two parts to the city really, the old town that you always see in the tourist pictures, and the new town, where the majority of the hotels and the main port is, it's probably half a mile/a mile between the two, but there's regular buses going back and forth between the two.
It's nice enough but there's not a huge amount to do/see, the usual streetside cafes/restaurants to sit and watch the world go by, or you can go to one of the islands off the coast. You can also walk around the old town walls and spot the bullet holes that are left from the upheaval in the early nineties! Most of the beaches in the area are rock outlays or pebble beaches, one of the few sandy beaches in the area (Sunj) is on Lopud.
I stayed here : http://hotel-ivka.com/hotel-ivka-engleski.htm the first time I went (2008) and it was fine, clean and tidy and not too dear.