Mobile is going to be your closest and best bet for solid courses. About an hour away from Biloxi, it's got half a dozen or so courses with decent ratings. I've played three in that city: University of South Alabama and Langan are both quality, and Cottage Hill is pretty solid, too.
Another hour east gets you to Blue Angel Park: three 18 hole courses on site combine for the single best destination in the immediate area. They're great courses that give something for everyone; if you only make one trip from Biloxi, I think it's a no brainer to make it be Blue Angels.
Hattiesburg also has some decent options from what I've heard, though I haven't been yet. It seems like it's a little over an hour from Biloxi. Paul B. Johnson up there gets talked about the most.
Beyond that, you're looking at a few hours drive to get to Jackson, which is great if you're up for making the trip.
As others have already said, Hiller is the local course. I wasn't a fan, to be honest, but wouldn't mind having it as a home course for a few months. Decent amount of variety given the terrain.
I've got reviews of many of these courses if you want some more in-depth thoughts. Enjoy Biloxi; unfortunately, it'll be HOT while you're there.