For some great Alpine hiking, throw some Alpen in your rucksack and head for the Refuge de Valmasque in the Parc du Mercantour, which is a little north of Nice. Take the train to Saint Dalmas-de-Tende, which is a pretty empty and not very friendly town in the middle of nowhere. From there, you can catch a bus to Casterino (it pulls up outside the train station, but there are only about 4 a day, so check the timetable). From Casterino, hike north (30mins) along the tarmac road, until you reach the carpark at the edge of the Parc du Mercantour. Then follow the yellow signs for the Refuge de Valmasque (2hrs 30 mins from there). There are spectacular mountain views and lots of wildlife (Marmots and Chamonix) to see along the way.
From the train station to the start of the walk
The walk to Refuge de Valmasque
The refuge is on le Lac Vert, it's a really great place, run by very friendly people, who might even take you for a moonlit swim in the lake if you are lucky.
You can leave the bags there and head out to do a circuit taking in some other lakes (including Lac Gele), and the steep peak behind the refuge. I think it's called Cime Chamineyes, it's about 3000m high. The views from the top of that peak are really amazing, and it's a little terrifying standing on there looking down on everything.
The lakes are all amazing, so clear and clean, and good for swimming to cool off after the climbing. From left to right, these three are Lac Vert, Lac Noir and Lac du Basto. The Refuge de Valmasque is on the other side of Lac Vert.
These two lakes are higher up than Lac Gele, and the water in the blue one (the nearest one) is bloody cold!
It's easy to get there from Nice. It's a great trip. Just don't fall off.