<map lat='43.704615274467294' lng='7.260322509765625' zoom='11' view='0' float='right'/> Nice is a city in France. It is fairly easy to get out of it, which is the main positive thing.
East towards Italy
Catch the bus #6 to the stop Bon Voyage (costs EUR 1.00) or walk from the city towards the motorway signs (A8) along the river with no water, it takes about an hour. The motorway is above you, go to the onramp that says to Menton and Monaco. Plenty of room to pull over, and cars are going pretty slow. When going to Italy, wait for a car going at least to Menton (or use a sign), then ask to drop you out at the first petrol station (the only one between the two cities) shortly after the exit to Monaco, and look for drivers going to Italy there.
If you're left on the péage Nice-Saint Isodore close to the Allianz Riviera stadium a lot of cars that come from all over France will stop there on their way to Italy. Passing the border might scare some people, and it's also true that hitchhiking is not as easy in Italy as in France so expect to wait a bit longer.
Take a train or the bus No 10 to St Laurent du Var - Gare SNCF. From the station building north of the tracks walk along rue Léonard Anfossi. Soon you will arrive to a roundabout, follow on, pass under the motorway bridge, where you'll see a second roundabout, the exit on your left is the onramp for westbound A8. Use a sign saying Cannes and get off at the petrol station on the Cannes bypass.
Both west and East on the A8
There is a péage in northwest Nice suitable for both directions. The problem though, is that it's difficult to access. Take the bus no.9 to Nice - La plaine and from there hitch or walk the remaining 2,5 km north along Route de Grenoble. Firstly, the motorway will be parallel to the road on your left, there you'll be able to see the southbound péage but unable to access it. A bit further is a roundabout with an on-ramp for A8 towards Monaco/Menton with a péage a 100 m further. To get to the southbound péage you'll have to keep north on Route de Grenoble (use the left shoulder), cross the A8 under the bridge and you will see a southbound on-ramp accessible only to cars coming from the north. Walk back along it till you get to the péage (although that's probably forbidden).
North towards Grenoble
That's a mountain road, where you can make it to Grenoble in one day or less (in summer). The first way to get there is the same as for the Péage on the A8, but from the roundabout just hitch towards Digne instead the A8. Other possibility is to take the "Chemin de Fer de Provence " train to Bellet, (at least 1 train an hour) there is a good roundabout just next to the station.
If planning to go to the Mercantour National Park, you can take a public transport bus from Route de Grenoble that goes to Saint-Martin-de-Var and costs as the normal ticket. There is a roundabout just at the end of the village.
When considering hitching in and out of Nice one should keep in mind that the bus company Lignes d'Azur operates lines to and from nearby cities (Grasse, Monaco and more) at a price of EUR 1.50 per single ticket (tickets are bought from the driver. prepare the exact sum). This buses have a LOT of stops and take a long time to reach their final destination but they are frequent and operate on Sundays. You can find the list of lines here.
It is possible to pitch a tent on the beach west from the airport just across the river. A perfect hidden spot where you can find ducks, couples having picnics, kids drinking beer in the evening and some fishermen but they will all leave you alone. It can get crowded in peak season... To get there walk about 2 hours along the beach towards west until you pass the airport and cross the bridge. Go right immediately and walk along the river until it touches the sea. Or take the train to Saint Laurent du Var. There is a huge shopping mall on the beach. Behind it there are big rocks stacked in a wave defence wall. Cross it and enjoy.
Another good option to pitch a tent in the north of Nice, very close to higway A8. On the end of the Boulevard Comte de Falicon you will find a church (last stop of the train Henri Sappia or previous Comte de Falicon). If you stand in front of the church go around from the left side and you will see small ravine between church fence and highway fence with small trees and bushes. It's enough place for a couple of tents and nobody will see you. It's quite noisy because of the road.