The old town area is entirely forbidden to the car, only the stop will be authorized until 10AM. Nevertheless, several paying or free solutions are offered to you.
The free car parks at Fort Carré and 11 November are close to the old town.Access is free during the day and night.To reach the old town, a shuttle bus (line 14) runs every 10 minutes from 08:00AM to 19:00PM or 10 minutes walking along Port Vauban.
To get there, take the Avenue du 11 Novembre along the port Vauban towards Nice.
The car park du 11 Novembre it's just before the Fort carré on the left.
The car park at Fort Carré is opposite the stadium (turn left at the red light).
It is also possible to park in the streets near the old town. The street parking is free during between midday until 2PM and free the evening between 6PM to 9 AM.
The underground parking QPARK Pré aux pêcheurs is very close to the apartments (2 minutes walk)
Prices vary according to the season and it is possible to consult the rates on their website QPARK.
I recommend booking online for better deals.