Just for your info, the fireworks start at 22:00 (10pm) and are shot from Piazzale Michelangelo.
If I’m there in the 24th I try to go at the Chalet Bellariva, along the river Arno. Actually I eat there a lot regardless of the day, because it’s a great place to eat. My cousin is a good friend with the owner, so we generally have no trouble getting top tables in the garden, but the place in summer is packed on a normal day, so on the 24th of June the place is sold out, always. If you can get a reservation try (contacts below).
http://www.chaletbellariva.it/contattaci/
Other well renown places I know are roof top bars/restaurants, often part of hotels. Some names:
La Terrazza del Brunelleschi (roof top restaurant of Hotel Baglioni)
Hotel Minerva roof top restaurant
Grand Hotel Cavour Divina Terrazza (roof top bar)
L’Antica Torre hotel Terrazza roof top bar
Sesto on Arno (roof top restaurant on the 6th floor of the excelsior hotel)
Of the above I’ve eaten only at Sesto, which is a full restaurant. The others I’m not sure if they are just bars or also full restaurants. I’m sure they all serve some food on that night.
Another place I’ve been for the fireworks o “Fochi” in Florentine (Pronounced “ Fo’hee” since Florentines pronounce a hard c like an h) is the Bar Il Tempio, basically a kiosk on the gardens of the Lungarno Del Tempio. It’s not a restaurant, but you can certainly get drinks. Another outdoor bar/kiosk is the Easy Living, at the Torre di San Niccolo (Piazza Poggi) The two spots above are probably the best spot to see them (not full restaurants though, just drinks).
At the Piazzale itself, there is the Ristorante La Loggia. I’ve seen the fireworks there but not on the 24th, of June, rather on New Year’s Eve of 2000 (on Dec 31, 1999). For that millennial occasion fireworks were shot from all hills surrounding Florence, not just Piazzale Michelangelo. It was the most amazing display of fireworks I’ve ever seen to date. Check if that is a possibility for the 24th of June. The Piazzale is generally closed to traffic on that night, so you might have to walk upthere unless you go earlier.
Take your pick. Just to let you know, finding a seat in any of them is going to be a major challenge on that night.