I've never been, but based on what I've read I think Limoncello would be an excellent choice. And if you want to go elsewhere for dessert, there are two well known Italian pastry shops on Hanover Street, the "main drag" of the North End neighborhood in which Limoncello is located: Mike's, the better known and larger of the two, but also the more touristy and less well regarded; and Modern Pastry.
As for Finale, their desserts are beautiful, and tasty, but unfortunately more beautiful than tasty. But still they're good enough to eat and served in a setting that a 16-year-old might enjoy, not because there's anything kid-like about the place, but because it might make her feel a little sophisticated (especially if she were allowed to order a decaf espresso with her dessert!).