Hi Blair, Yeah I went in June last year. You'd have to go out of town to get a decent run in, however, the best options in Noumea are Ouen Toro near Anse Vata or up to the zoo in the north of town.
Are you there on the 6th May? There is an orienteering event on. You'll probably need to pre-enter.
On our spare days in Noumea we went out to the nearby islands including Ile aux Cannards which had a marked underwater snorkelling trail. Regular water taxis run between Anse Vata and the islands, the taxis leave when they get full (4-6 people) and you can get snorkel gear on the island. There are literally 100,000's of fish and even turtles.