Last time down we met and talked to folks that were staying at Jennies Place and they said it was very nice, at the north end of Grande Anse and in your price range. Here's a link:

http://jennysplacegrenada.com/about.html

Regarding Mourne Rouge, I've "heard 2nd hand" some people complain about noise from a nightclub late at night. Just sayin' you might want to research that a bit if you're thinking of staying over there.