Cinque Terre seems to be the tourist destination of North American visitors, but I wouldn't say it's the gem of Florence. To me, Il Duomo takes the cake as one of the most spectacular vistas and architectural sites.
It doesn't get better than a view from the dome of one of the most magnificent cities in Italy. Down in the alleyways, there is a bit more of an overflow of tourists and tourist traps, but it still remains a gorgeous space. The Uffizi palace is a mine of great art, and the Loggia has some wonderful replicas. Florence is also home to some deliciouis gelato, Carapina, and a wonderful little restaurant called the Trattoria l'Oriuolo. If you are a market centric person, Mercato Centrale is a good little hideout. The other excellent view comes from the Piazzale Michelangelo, where you can view the Ponte Vecchio along with every architectural marvel in the city of Florence. Along the way, there is a fantastic little panino shop, Il Panino del Chianti, which served as an excellent quick bite.
This declaration will be controversial, but I don't care. Cinque Terre, while very nice and very pretty, is not the dreamland that the photographs make it seem. A lot of the houses are rundown, and the colors are definitely not very vibrant. But, the walk from Vernazza to Corniglia is wonderful. I would recommend spending the time to walk all of the villages (or at least the paths that are open) if you can manage it. Taking an early train from Florence to the regional train makes it very difficult to spend a lot of time in Cinque Terre. We had about an average of an hour in each city. Skip Riomaggiore and Monterosso al Mare... to me, they are the most touristy. I would say Corniglia seemed the most interesting, but the walk up from the train station takes at least 30 minutes. Definitely take the path from Vernazza if you want to enjoy a peaceful cliffside walk.