This is what we know so far as where the concerts will be hosted on December 31st, 2016 to welcome in the New Year:
-- main concert -
Marco Mengoni (Italian pop music) @ Piazzale Michelangelo
-- classical concert - Orchestra da Camera Toscana
@ Piazza della Signoria, under the Loggia dei Lanzi
-- gospel music - Music Pool
@ Piazza San Lorenzo
-- jazz and bebop - Music Pool & Musicus Concentus
@ Piazza del Carmine
FOR KIDS - not in the historical center, but in residential areas
-- circus acts - jugglers, minstrels, marionette puppets by Aria Network Culturale @ Piazza Bartali (Gavinana area) - not sure when it starts
-- entertainment for kids starting in late afternoon & folk and swing music later at night @ Piazza dell'Isolotto
All these concerts are free.
AS FAR AS MOBILITY INTO THE CITY: we highly recommend you
NOT DRIVE INTO THE CITY!
While official details have not been given about the ZTL, in the past the ZTL remains ACTIVE all night long on the night of December 31st so you CANNOT DRIVE into the historical center that night.
There are so many people out and about, you wouldn't want to attempt it -- and you won't find any parking, either. I would go crazy driving around all of the people who spill out on the streets so I don't recommend getting anywhere near the center.
From SIGNA, where you are based but I would offer this tip for all others planning to come into Florence, the best option is to park in the area of Scandicci (I would suggest the parking at Viale Nenni) and then
take the TRAM into town. Here's a map of the tram line and the parking areas near each stop along the line. The one at viale Nenni is the largest parking so more likely you won't have problems with parking there:
http://www.gestramvia.com/linea-e-parcheggi
The tram takes you all the way into SMN which is in the center and walking distance from the 3 main piazzas holding music concerts -- as well as where most of the sights in Florence are located.
Usually on the 31st of December, the tram works ALL NIGHT so that way you can head back to your car when you're ready to leave back, again taking tram back from SMN. Now, if you choose to be up at the Piazzale for the concert there, the walk back to SMN is a hike (the piazzale is on a hill overlooking Florence) - and you might want a taxi back. But with people and traffic, walking might be faster than a taxi

.
As far as restaurants -- YES, I would suggest you decide on a place and book as soon as you know where you want to go. Some places will offer a large, fixed price menu and limit seating for the night where you can stay all evening.... but others won't, serving regular turns throughout the evening. In any case, better to book and have a place already picked out rather than walk around and be turned away if all seats are taken.
ENJOY the end of 2016 in FLORENCE and welcoming in 2017!!