A neighborhood built around the church and piazza of the same name, Santa Croce is just south and east of the historic city center of Florence and proves to be a less expensive, less crowded alternative. The 13th century basilica, known for the famous Italians buried here (Machiavelli, for one) and the gorgeous art in the interior, and its place as the largest Franciscan church on Earth, is the central cultural institution, although those with an eye on nightlife and cuisine will find that they need not stray too far.
The nightlife scene near the Piazza Santa Croce may be the most intensive in Florence, particularly around the intersection streets of Via de' Benci and Corso dei Tintori. This is where you'll find younger generations drinking to get drunk in a dozen or so bars, including the cocktail stylings of Moyo, the American touches of Red Garter, and the darkly-lit Oibo. The piazza itself also stays abuzz until late into the night, especially when it hosts events, which happen with frequency.
As far as good eats go, you've got everything from Middle Eastern to Japanese to American here, but (as you'd suspect) the classic Italian specialties are the most worth hitting up. Two gelaterias in particular are worth mention: Vivoli on Via Isola delle Stinche and Gelateria dei Neri on Via dei Neri. You may never want to eat solid food again. If you do, try the cheap and palatable Trattoria Anita, which is hidden away on Via Vinegia or the Osteria de' Benci, located toward the river from Piazza Santa Croce.