I know a lot of tourists who visit the clothing market of Quatre-Bornes for some good deals....I can't remember but I think it's on a Sunday.
Make sure that you visit the Caudan Waterfront and other streets in the city as well. Since you're coming through the customs at the Airport, you can check the clothes from makes like (Lacoste, Ralph Lauren) which have got duty free shops there and in some towns.
It depends on what you meant by cheap...and then you have to compromise with quality!
If you are looking for shirts for your husband, there's a factory shop in the end Ollier Road, Quatre Bornes. They used to sell really good shirts (Marlboro Classics e.t.c) at affordable prices around Rs 500 but the inside tags have been cut (it doesn't matter anyway).
There was another topic where some shops have been mentioned, try looking for it.
Hope this helps
I'm coming to Mauritius in December to replenish my clothing stock as well and perhaps sell some on Ebay.