Mississippi is behind when it comes to the craft brewing game due in part to archaic regulations on alcohol percentages and the ability to sell canned/bottled beers directly at the breweries. However they have slowly been relaxed over the past 10 years. With that said, we have some good local breweries within a short distance of Hattiesburg/Biloxi.
Southern Prohibition (Hattiesburg, MS)- Try FireAnt, Suzy B, Crowd Control, and Devil's Harvest. Great taproom in Downtown Hattiesburg, Mercury Pizza Co. typically has their food truck parked outside on weekends.
http://soprobrewing.com/beer
Chandeleur Island (Gulfport, MS - approx 1 hr away)- Try Lil Miss, Lil Smack, and Surfside. Small taproom in Downtown Gulfport. Typically has a lot of rotating/new styles to try and are always doing something different. They have a lot of the lighter summer beers, sours, etc. if you're into that.
https://chandeleurbrew.com/p/beers
Lazy Magnolia (Kiln, MS - approx 1 hr away)- Try Southern Gold (USM themed beer), Belgian IPA, and Southern Pecan (their signature beer). Mississippi's oldest brewery in the hometown of Brett Favre. I haven't been there yet, but I've heard their taproom is top notch with live music on the weekends.
https://www.lazymagnolia.com/our-beers/
Biloxi Brewing (Biloxi, MS - approx 1hr 15min away)- Try Biloxi Blonde, and Salty Dog. Smaller brewery in Biloxi. Walking distance to MGM Park (for the CUSA tournament). All of their beers have some sort of coastal tie-in/theme (much like Chandeleur). Also, Mississippi Brewing currently brews their beers out of Biloxi's facilities. Haven't had the chance to try any yet.
https://www.biloxibrewing.com/beers/
Slowboat Brewing (Laurel, MS - approx 30 min away)- Try Into the Mystic and Dairy of a Madman. Small brewery in Laurel. Has really stuck to their three main brews, but Into the Mystic and Dairy of a Madman are among my favorites.
http://www.slowboatbrewco.com/drink-slowboat/
Additionally Jackson, MS (about an hour and a half away) has Luckytown Brewery and Cathead Distillery (Gin and Vodka)
Bonus:
Keg and Barrel (Hattiesburg, MS) - Pub style restaurant which had (at one point) the most beers on tap in the state. Most of the taps rotate weekly with local, regional, and national/international beers.
The Porter Public House (Hattiesburg, MS) - Pub style restaurant with a large amount of taps, and good beers/drinks/food.
Double Secret Bonus: Since I'm a recent New Orleans resident: Urban South, Courtyard Brewing, and Wayward Owl Brewing are also great places with great beers (among multiple others).