First, check this :
http://www.wannasurf.com/
Then, if you want to surf without a car, just find a spot you'd like to surf (depending on your surfing capacities) and find an accomodation in the place. There are buses, but not that much and traffic jams are a plague in Réunion.
You could stay in St Leu : I recommand the guesthouse named "Dodo spot" : it's right in front of the fabulous wave of St Leu, just the road to cross and some paddling in the water ! Amazing. However the place is a bit expensive (around 45-50 euros / night ??). From here, you could carhitch to "Trois Bassins" some 15 minutes away (good spot, works more often than St Leu)...