Sarajevo is a great idea for an overnight trip. Sadly, many of the major museums/attractions are still closed for repairs, but the old turkish quarter is really worth seeing. The food is much cheaper than in Dubrovnik, and the coffee is better. There are a couple of daily buses from Croatia. Mostar is also quite nice, but smaller than Sarajevo, and with much more pronouced ethnic tensions.
Kotor and Cetinje are the places to visit in Montenegro, lots of historical sites and buildings to poke around in. There is a daily bus from Dubrovnik to the border (change buses, the montenegrian bus is waiting at the border) which continues on to Herceg-Novi, and then along the coast. Although northern Albania is supposedly beautiful, tourist infrastructure is essentially zero, and the northest of the country near Kosovo is still very unsafe. Enjoy Dalmatia and do an one or two night excursion to Sarajevo would be my recommendation.