One of the great things about Nice is how close the airport is to the city – just a 15 – 20 minute bus ride direct into the centre along the palm-tree-lined Promenade des Anglais.
On your flight out of Nice the airport is a pleasant place to await your flight. If you have time before going through security go along to the upper level by the KLM desk and go up the very long escalator (or in the lift) to the top floor where you’ll find several cafes and a bar – with a wonderful view of the arriving and departing planes.
thebestplaceinfrance 
I agree, Nice Airport is so handy for the city and the transfers are cheap too – just 4 euros on the bus and as you say, and short and scenic ride to the centre. Big bonus for getting the holiday off to a good start!