There's hardly any point in going to Copacabana without a trip to Isla del Sol. Boats leave around 8:30 AM for full day tours with stops at the north and south of the island. Half day tours are also available in the afternoons, typically visiting just the south.
But since most tourist rush to the island after arriving and travel on to either La Paz or Peru, the town itself is pretty quiet during most of the day and makes it a nice place to chill out for a while.
Walk all the way to Yampupata. It's about 17 kilometres or 4-5 hours, along a dirt road with a few ups and downs and very little traffic. The scenery on the way is superb. If you don't want to continue to Isla del Sol, it can be kind of hard to arrange transport back. A better option is probably to go there by car/bus/truck and return on foot. This also brings the advantage of walking with the sun mostly in your back.
