It is about a 15 minute ride from the airport to one of the last stops along the Promenade des Anglais. From this stop, it's about a 10 minute walk to many apartments in or near old town, and you can see the famous Hotel Negresco as yo look down the promenade.
The Promenade des Anglais is a wide, paved, seaside walkway where locals and tourists walk, jog, bike, and rollerblade. The promenade follows the Mediterranean Sea along the shoreline. Although it is a rocky beach and the water is quite cold in the winter months, we like to sit on the beach to soak up the sun and listen to the sea. The water makes an amazing whooshing sound when it gets pulled back away from the shore through the rocks.
Nice has a lot to offer, from it's charming seaside sunny weather, to gorgeous architecture in and around it's old town, to excellent French and Italian Restaurants located all over the town. Nice has a few unique landmarks to visit, but we love it mostly for its small-town charm, excellent weather, and proximity to many other beautiful small seaside towns along the riviera.
Two years ago we stayed just outside of old town, and this year we got an apartment right inside the old town, just off of Cours Saleya, which is the main road off of the Promenade des Anglais that sits on the edge of old town. Cours Saleya is the location of the daily flower market in Nice. At the end of Cours Saleya, sitting on the edge of Castle Hill, is a beautiful old yellow building where the famous painter Matisse lived on the third floor.The market in Nice runs every morning along Cours Saleya and offers lots of Provençal items, including beautiful flowers, fresh bread, cheese, and produce, as well as more touristy items like jarred oils, herbs, and candy.
On Mondays, different merchants make their way to Cours Saleya, as it becomes a large Bric-a-Brac market, where antique tables occupy the entire span of Cours Saleya.
Cours Saleya is one of the main entrances to Nice's old town, which is one of the larger and nicer old towns in the area. The old town of Nice is a maze of twisting streets and alleys, boasting a wide array of merchants and merchandise.
There are many shops with touristy goods for which Provence is famous, such as soaps, bath salts, and dried herbs. There are also a large number of shops to get food, including amazing fresh pasta, sauces, cheese, and meat. There are also loads of excellent bakeries, wine caves, and restaurants. It was a daily ritual for us to enter the old town and wander it's streets, just to soak up the atmosphere and get lost in it's streets.
Just a couple blocks from Cours Saleya is a daily fish market, lasting until about lunch time, in a beautiful square in old town. It smells a bit like fish, but if fresh seafood is your thing, this is a great spot. Another great area of old town is one of the main entrances to the area, and also a main entrance to Castle Hill. This road contains many restaurants and bars, and leads into a large square with a beautiful church.
Castle Hill sits on the end of the Promenade des Anglais and serves as a separator between the old town of Nice and the large Port area on the other side of town. On top of Castle hill you can find some ruins from the old castle, a sizeable waterfall on the side facing old town, and a large park for children to play. It is a large area, with many sloped roads and stairways, offering many different views of both Nice's old town and port areas. It is a great way to spend an afternoon or a whole day. 
Or, if you are like me, you would venture at least partway up the hill every morning and/or evening to catch the sun rising or setting above the beautiful city. In the morning, the sun rises over the port side of Nice, shining a soft light on the buildings facing the Promenade des Anglais. In the evening, the sun sets over the water sea near the airport, providing a gorgeous colourful sky as you look along the Promenade stretching through Nice.
Something neat about Nice and most of the nearby towns is that it has a large Christmas market that takes up most of Place Massena, Nice's largest and busiest square. The Christmas market runs for about two weeks during Christmas and New Year's, and hosts many vendors, selling mostly food and hand-made gifts. Many of the items are the same at most town's Christmas markets, so it's not necessary to go to them all, but it is a cool experience to check out the large market in Nice. The atmosphere is great, with lights and music, a ferris wheel and other small rides, and a small skating rink.
Aside from old town, there is some great shopping to be had in Nice. Starting in Place Massena, there are three areas that we frequent for shopping. The first area is one street off of Place Massena, closer to the water. Rue Saint-Francois-de-Paul is the smallest of these areas, and it has the most boutique-style shops of all three areas. Here you can find one-of-a-kind stores such as a chocolatier, an olive oil store, and some great smaller shops selling soaps and other unique gifts.Rue Massena, which turns into Rue de France, is a wide mainly-pedestrian street that runs far from Place Massena, in the direction away from old town, and has many shops, bakeries, and restaurants. Each year, we spend most of our days in Nice wandering down Rue de France at least once, sometimes looking for lunch or dinner, or peaking into stores such as Occitane en Provence. For some other unique stores that are less frequented by tourists, Rue de la Liberte has some neat stores, and is just one street forth from Rue de France. Rue de la Liberte has an excellent tea shop that we visit frequently called Le Palais des Thes.
Avenue Jean Medecin runs along the tram tracks running northward from Place Massena. Most of the stores and restaurants along this road are chain retailers, so the shopping and deals can be great, but not necessarily unique. There is a Galleries Lafayette where Jean Medecin meets Place Massena, and lots more shopping until you hit the mall, Nice Etoile, further up the road.
The great thing about Nice is that so many small towns are less than half an hour away, and you can get to most of them by bus, train, or car. Almost every day, we would find a small town nearby to visit. For one euro, you can take the bus to almost any nearby town, but it is much slower than the train. My wife and I take the train everywhere. We hop on the tram at Place Massena and take the tram north until we pass the shopping mall, Nice Etoile. From here, the train station is only a few minutes' walk away, and we could get to most towns for between 10 and 30 euro for a round trip. Trains for most towns leave every half hour or so, so the train is pretty convenient. Most of the time, we would take the train to a town and visit it for the morning, and then stop in another town on the way back for the afternoon. This way, we payed the round-trip price for the town that is further away, but we did not have to pay to see the other town.
Antibes a about a 30-minute train ride west of Nice. It has a really beautiful walled old town and a very large covered market each morning. There is also a large Picasso museum and a large old castle, Fort Carre.
Villefranche is about 15 minutes east of Nice by train. It has a Venice-like waterfront of shops and restaurants, and a beautiful harbour, large fort, and nice old town.
Eze is a wonderful perched medieval village just past Villefranche. You can take the bus or walk up the mountain to see the unparalleled old town and gardens atop the mountain, as well as the Fragonard perfume factory, where you can take a tour and visit their shop.
Monaco is the second-last town east of Nice. There is an excellent oceanographic museum built right into the cliff on the sea, a neat old town and palace, and an enormous port with even more enormous yachts. The Monte Carlo Casino is a must-see, and so are the cars parked outside.
Menton is the last town before the Italian border. It is about 30 minutes east of Nice by train. It has a small but charming old town, a large cemetery above the town, and a lot of great restaurants along the waterfront.
