For a day-excursion out of Nice, take the train up in to the mountains. The train is tiny and runs on a single track from central Nice to Digne. We actually jumped off half-way in Entrevaux, about one hour from Nice. This is a walled medieval town with a fort that you can walk up to (entry fee €3) – it's a bit of a climb, but the view is well worth it. The town and the fort were deserted when we went in March – but probably gets busy in summer. If you go out of season, I recommend to bring a picnic as there might not be any cafes open.
If you don't mind travelling a bit further, Digne, which is ment to be beautiful, is three hours from Nice. Just make sure you check the time table – the trains only run about six times per day.
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