The place to be seen would have to be the Spanish steps. This has been a local hangout place since the 18th C when it was built by the French but named after the Spanish embassy in the piazza. Check out Keats's house, on the right of the steps looking up, where he and his romantic contemporaries like Bysshe and Shelley gathered or just hang out yourself on the steps and people watch . You could also spread your mates around the steps and take a 'Where's Wally?' shot.