In the heart of Old Havana, you'll find the restored Spanish-influenced beauty of a public square called Plaza Vieja. This was once the place for the wealthy elite to look down from their balconies on the great events of the city: grand parties, parades, speeches, even public executions. Nowadays, the once-failing area has been revived and the colonial architecture bears a sheen that invites foreign money to lounge about and watch the world spin on. And it's totally worth it.
Old Havana itself has been labeled a UNESCO cultural site and it can be argued that there really isn't a more self-aware and tourist-driven area in the city. It's no different in Plaza Vieja, which has seen a steady clean-up and revival effort since the 90's. Grab a world-class coffee at El Escorial or a beer at one of the other cafes along its periphery and relax with a view reminiscent of Europe or climb the five floors to the top of the Camera Obscura exhibit (360 degree camera for a 2 CUC entrance) and enjoy the view from the terrace. It'll be a bit more expensive than some other parts of the city and expensive boutiques and clubs may mar your romantic notion of how a historic city plaza should operate, but you'll not see panhandlers or tour buses despite just being a few blocks from the ferry terminal. And that can be a big plus in itself when visiting Cuba.