At NCE, stay airside—terminals are spread out and security lines fluctuate, so relax near your gate.
Take tram line 2 from Terminal 2 to Jean Medecin stop (35 minutes, EUR 1.70). Walk 5 minutes east to the Promenade des Anglais. Spend 30 minutes on the beach and the seafront walkway. Head back at the 90-minute mark. If you have 5 hours, add 45 minutes in the Old Town: walk east along the promenade from the beach to Vieux Nice.
Follow the tram to Jean Medecin, then walk to the Old Town. The Cours Saleya flower market runs until 1pm Tuesday to Sunday (free). Grab socca and pissaladiere from stalls in the market for under EUR 10. Spend an hour in the Colline du Chateau park above the Old Town: free entry, good views of the bay. Descend to the beach for an hour before heading back.
With 10 hours, take a 25-minute bus from the center (or a EUR 2 train) to Villefranche-sur-Mer for a calmer beach and harbor. Alternatively, the express bus to Monaco takes 45 minutes and costs EUR 2. Monaco's harbor and the casino square are 10 minutes on foot from the Monte-Carlo bus stop.