When in Copacabana, do not pass go, do not spend $100. This place is a hole. Noisy, boring and aside from a Moorish cathdral - pretty damn ugly.
Jump straight on the boat and head straight to the gorgeous Isla del Sol. It's a very traditional island in Lake Titicaca where electricity is scarce, you'll have to wait for the restaurant staff to catch your fish before you see your meal, and the showers are rarely hot. That aside, it's a really stunning place. It's surrounded by the deep blue shimmer of Lake Titicaca, with the moon reflecting on its surface at night, and the snowcapped peaks of some distant Andean mountain range rising on the horizon.
There's great hiking opportunities (takes 3 hours to walk from one end of the island to the other), some half-decent archaological remains, lots of accommodation and it's worth staying a night or two. Oh, and there's even an internet cafe here now (really fast connection!) so you can update your blog from the birthplace of the sun!