I live in Panama City. While we would welcome you for New Years, do not plan on swimming in the Gulf of Mexico. A nice day in December or January will see a high near 70. The low is sure to go below 50. The water temps would certainly tempt a polar bear. Humans, not so much. A not so nice day would mean temperatures did not get over 40. You don't want to be here then.
Pier Park in Panama City Beach does throw a nice celebration. They will drop a giant beach ball at midnight as well as 10,000 of the real thing. This takes place at Pier Park, a huge outdoor shopping center with theatres, shops, restaurants and bars across from the beach. It's a nice place to watch the sun set. You would not be alone as thousands will join you. It's a very family friendly destination (especially since Spring Break has had a stake driven into its heart).
There is a very nice state park there, three piers (one about 1/4 mile long), fishing, boating, loads of good restaurants and bars (although fewer in winter). But the main attraction is the beach and it's iffy that time of year.
Pensacola is a larger city with more to see and do as well as hundreds of years of history. I'd recommend it over PCB. They're only two and half hours apart so you could see both if you wanted (as well as Destin and Ft Walton Beach, etc. in between). But if you want to swim, go to Miami.