Another new country! I had heard terrible things about Copacabana, that it's not a nice place, don't go there, nothing to do or see if you've done Lake Titicaca already... However I disagree!
I was only there for one night and I wouldn't necessarily stay any longer but I think I would have missed out if we didn't stop here. We had already seen and done the lake from the Peruvian side and spent time on the islands too, however it's much more picturesque and scenic from Copacabana. Puno is a big city and detracts from the lake somewhat whereas Copacabana, less developed and set on a hill gives you a much better Birdseye view.
We stayed in La Cupula which is a hotel and a hostel from what I can gather, we stayed in a private room but shared a bathroom. Although it calls itself a hostel, it feels much more like a hotel. There's a hot tub onsite, llamas/al pacas roaming around and a beautiful garden with statues, seating and hammocks to soak up the very strong sun!
There's also an onsite restaurant which is amazing and great value for money; I chose a cheese fondue for one and it honestly could have fed at least four people but it was amazing!!!!
In Copacabana itself, admittedly there isn't a huge amount of things to do but it's a nice place to relax. Lots of rooftop restaurants and bars which overlook the lake and it's nice to watch the boats coming in and going out. It's also slightly more tacky than Puno with zorbing balls, pedalos, rental boats and jet skies however it's at the far end of the port so easily avoided.
Of course if you haven't already visited Lake Titicaca there's plenty of boat day trips available. There's lots of shops and tourism markets with clothes, handicrafts etc. A large cathedral and a couple of parks but by far the most popular attraction is the port/lake with its view and a large anchor monument on the front!
Definitely worth stopping for one night but probably not much longer - a nice place to relax and great for food and drinks!