From Arequipa, i got a bus straight to Puno, 6 hours trip. I didn’t like Puno very much, the people isn’t as friendly as in the rest of Peru and there isn’t much to see in the city itself. I did the Uros Island tour, which was interesting, but quite tourist. If don’t have much time, you can just get early in the bus station, book the first tour from 9:00 to 12:00 and get the bus 14:30 to Copacabana (it’s the last bus if you want to cross the border). You will pay around 15 soles (12 reais) for the bus tickets with Titicaca bus plus 20 soles (16 reais) for the tour. Get ready for the “emotional games” to get your money in the island.
I’ve heard that the other two islands, Taquile and Amantani, are nicer and less comercial than Uros, if you have enough time you can try it, you can even sleep in one of this islands.