Noumea is a popular port of call for people sailing around the Pacific, though most dare not sail during cyclone season. There are Water Taxis that operate from Anse Vata that can take you out to the nearest small island.
The Little Train (Le Petit Train) is a motorised tour on normal roads, that runs several times a day. It is an area tour, but you can also hop off one train, and catch the following service. Check the timetable, though, because it may be cancelled or only offer two services on a given day.
The city is also serviced by 8 colour coded bus routes that costs 210 CFP if you buy your ticket on board (as of January 2010, still valid May 2014), or 190 CFP if you prepay. Others have recommended this only if you feel your French is up to scratch, as the bus drivers very rarely understand anything but French. It is sufficient to know that the bus goes to "Centre Ville", then hand over the money and state the number of tickets required (une personne, deux personnes, trois personnes, etc.).
You can buy a number of tickets in advance at the office on rue d'Austerlitz (it's more of a booth, actually) but you need to validate the appropriate number of tickets for the trip when you board the bus (that includes the ones you buy from the driver). Validation just means inserting them them into the yellow ticket machine located at the front of the bus. There is a ticket stand at the Moselle transfer station (located next to the cinema's) and also one located at the edge of the town centre at Place Roland. The bus line is called Karuia  and all the timetables and more information can be found on their website.
The first trick is to recognise a bus stop when you see one. These are white-ish pillars, usually with a name on them, sometimes with a shelter from sun or rain, but usually with no indication of the line(s) that stop there unless it has a timetable attached. Bus line 10/11 runs along the main beach road and is good for tourists as it stops at Anse Vata, Lemon Bay, a supermarket, the markets/harbour, centre of town (important for bus transfers to other lines), the maritime museum, aquarium, Ouen Toro and Kuendu Beach. Bus line 40 runs from Moselle Centre ville (located next to the cinema) to The Tjibaou Cultural Centre. This is by far the easiest tourist attraction to get to via bus since you just have to ride it end to end. Bus line 50 runs to the Zoo however you have to get off at stop Pervenches and walk up the hill to the zoo entrance.
Also available for tourists is a "Noumea Explorer" service that runs an hourly loop pass the major tourist sites (Museums, Parc Forestier and Zoo, Tjibaou and hotels) hourly. That for 1500CFP a day (March 2010 price), is a great idea to be used to explore each of the sites for an hour before catching the bus onto the next location when it comes past again. The service takes a little over an hour, the stops are hard to locate at the start, and you need both a map that shows the stops, and also a leaflet from your hotel or a tourist office that gives the timetable.
Most of the tourist attractions in Noumea are closed on Mondays and open all other days. with the exception of Museum of Caledonia that is closed on Tuesdays. Each venue has its own entry costs, but in 2010 for 1700 CFP a "Pass' Nature and Culture" could still be purchased that provided admittance to the Tjibaou, New Caledonia, Noumea and Maritime History Museums, Zoo and Aquarium that could be used over 6 months.
Another good idea, is to grab the Free English publication "The New Caledonia Weekly" and check in it for local events and ideas. The best map was the "New Caledonia Visitor map" found in many places. This is an A1 sheet that can be a challenge in high winds, but at least it shows you where the "Noumea Explorer" stops are.
New Caledonia is home of one of the largest Lagoons in the world. So naturally water sports are very popular.
Baie des Citrons is also very protected from wind, making it even more enjoyable for the novice. But also if you are prepared to pay for a water taxi ride, Ile aux Canards just off Anse Vata (maybe half a kilometer away) has a snorkeling track in a marine park that has even better coral to see. The visibility can be poor after rough weather, and the charges for almost everything are appallingly heavy (600 CFP for a chair, the same for an umbrella, and the service is surely the surliest found anywhere in Nouméa, aside from the Tjibaou cafeteria). You get there by water taxi from the lower level of the faré ("native hut") half-way along the Plage Loisirs or Anse Vata beach. The price in March 2010 was 1000CFP for a return trip, which was good value. It should be noted that seeing sea snakes is not uncommon in Noumean waters, but they are very unlikely to bite a snorkeler. Sharks are very rarely seen though. You can rent a mask, fins and snorkel for about 1000 CFP, so you may think it worthwhile taking your own.
The quickest way up from the area near Anse Vata is to walk along rue g. Laroque, but if you reach the pharmacy and the Hippodrome, you have gone too far. Go past the first couple of cross streets, then look for rue Paul Baumier on your right: there is a Gascon restaurant on one corner, and the Val Plaisance Charcuterie on the other. Walk up the street warily (the drivers are a bit wild) then pick up the track at the top end of the street. This leads up to the road that comes from somewhere past the Meridien hotel. The track is a bit of a scrabble, with a number of 5 cm stumps, but this mid-60s rambler got up it all right. Once you are on the road, you can either go west to look out over the sea or just look for the walking tracks that start immediately opposite. There is a painted map-sign there (we could not get any printed ones) so take some notes, especillay of the distances, because these are repeated on the track signage.
The main thing is to be aware that there are many other tracks than the ones shown, and the red tracks (on the signboard map) are indeed "difficult". In the late afternoon, we found plenty of other walkers and runners so the place is safe enough. Take some water, and watch where you put your feet, as twisted ankles are always possible on the loose stones and rocks. Keep an eye on where you are going so that you can retrace your steps, because the internal signs are poor. The views, however, are superb.
Most of Nouméa is also very close together, and safe to walk day and night between the suburbs. By day, the walk from Anse Vata along to and around the Baie des Citrons is pleasant. Assume that coffee and tea along the way will leave you little change from 500 CFP (each).
Food is not cheap in New Caledonia, but you can do well shopping at the non-tourist shops. Learn to detect the boulangerie and patisserie for bread and pastries, the charcuterie for meat and pâté and so on, but don't pass by the slightly seedy-looking general stores, where you can probably get tinned pâté, packaged cheese (wedges of brie, for example) and more.
At night, locals who eat out seem to wait until "vingt heures" (20.00 or 8 pm) before they eat, though most places are open from 18.30 (6.30 pm).
Views and food
The 360 Restaurant  is a revolving restaurant on top of one of the Ramada towers. At one point, you are looking straight into the apartments of the other tower, but the food is truly superb, and the lunch views are great.
The local beer is 'Number One', and it is a passable drop. There are many French wines to be had, but as a rule, the New Zealand and Australian wines seem to travel better (but that is an Australian opinion, and so open to being questioned). The local water is said to be perfectly safe to drink, but bottled water is easy to find if you are fearful. We stocked our hotel fridge from the neighbourhood general store and effected considerable savings.
Cappuccinos come heaped high with cream (not froth), and tea is served without milk. The hot chocolate is actual melted chocolate, not a cocoa-based drink, which you may find lovely or disgusting depending on your taste. Fruit juices are pricey but excellent.
Le Surf (www.grands-hotels.nc) Le Parc
Ramada Plaza, rue Louis Blériot, Anse Vata