Train or bus to Villefranche ( bus is cheapest ) if it’s warm and you like the beach . It’s a mixture of course sand and fine gravel and is stunning .
You could take a day trip to Antibes and Cannes. There is proper sandy public beach in Antibes called La Gravette and the old town is beautiful . If you buy a train ticket from Nice to Cannes you can break your journey in Antibes in either direction ( just remember to validate your ticket each time ) .
I second a walk to the top of castle hill in Nice Lovey cafe at the top . Amazing views ,
There is a linear park in the centre of Nice that has some lovely fountains you can cool off in, the flower market in the old town is really atmospheric ( it’s on in the mornings) and of course the Promenade des Anglais is a must . All these things are free .
If you fancy getting away from the coast the hilltop villages of St Paul de Vence (bus 400) or Eze( bus 82 or 112) are lovely and the bus tickets inexpensive .
We found it a bit tricky to find the correct bus stops in Nice at first . We now use a combination of the lignes d’azur website and google earth to pinpoint the actual stops before we go .
The train is much easier but a little more expensive . ( still very reasonable though)
You can buy strips of 10 bus journeys at the ticket office just out side the airport terminal which makes each journey even cheaper. You can buy your train ticket there too or from the station.
We found if we ate our main meal at lunch time it worked out much cheaper. Going to the supermarket to stock up on snacks/drinks will be loads cheaper than going into a cafe every time, especially with 5 of you .
Nice is a great choice especially with older teens . Mine loved it at that age .
Hope you have a wonderful time .