I have never been to the Peruvian Amazon region but Lake Titicaca I went to on a whim with Mrs Johnny and it was the best capricious moment I have ever had. You don't need 3 days there, overnight buses from Cusco in both directions and a full day tour of the Uros and Taquile is definitely possible so maybe you will have time to do both. Puno itself isnt a particularly pretty city.

If you are fancying going to Iquitos in the Amazon then the BBC's Lonely Planet Thorntree forum has bags of info on it