Went there a couple of years ago for Carnival. Started out in EZE on a 10 cruise and the boat ended in GIG and we used it as the hotel for 3 nights as Carnival went on.
Copacabana and Impana (sp) were stunning. The surf is so strong out there that no one actually gets in the water. They congregate in groups. So you get to the beach, find a gazillion people hanging out and locate a group you want to hang out with and look beautiful people. (just don't think of dp in the thong as someelse mentioned.) But imagine him with a bud light group.
Sugar Loaf Mountain has the "Christ" statue. When you get to the top of the base of the statue you have an incredible view of the city, ocean. I sat there and took in the views of the cruise ships coming in as well as watched the planes take off from the SDU.