In september I stayed with
Mauri Holidays, in an apartment at La Gaulette....10 minutes from Le Morne spots that face One Eye...U can book via booking.com...sori don'thave a direct email...it was modern, very clean and perfectly adequate, short walk to La Gaulette supermarket and cafe/restaurants.
and there are plenty of low cost perfectly good apartments in La gaulette, just google it
you'll need a rental car
also try firstname.lastname@example.org
Joacim Carlson has apartments closer still and is used by Kitethrills Aussie tour groups,
I have no direct experience but Im sure Mike at Kitethrills has sorted out good digs.
and if you really want to go troppo check in to the Riu, smack on the beach, everything you want...but at a cost
either way, you'll love the place, have fun!