We walked the walls in the late afternoon, about 2 hours before they closed and that was also a good time. We also did two tours out of the old town, both with Dubrovnik Adventures. One was a bike tour with wine tasting - easy biking until that last uphill where some of us had to walk for a bit followed by great bread, cheese, ham, olives and wine with opportunity to purchase, but no pressure to do so. The second was a kayak trip - away from town and just the two of us with the guide - we really enjoyed that. Other companies have kayaking right from the old town. Try to find and attend a concert in evening. We loved that. We just wandered and found a restaurant which was OK, and we had a drink at each of the two bars that you slip through the wall to get to.
Cable car, for us, a bit of a bust. We took some pics and headed back down. It's a nice view, sure, and there was an exhibit you could pay extra for at the fort, but otherwise, we didn't see what else to do. I'm not sorry I did it, but everything else we did was more fun.