I went to school in Jackson for 4 years and there's actually some pretty cool areas of Jackson if you know where to look.
The Fondren District is pretty fun and depending on when you go, you might run into one of their frequent block parties. It's a mix of art, music, food and shopping. You could call this area "Hipsterville".
Belhaven University's campus is half-a-mile away from Fondren and is potentially a pretty cool spot to kill time. Their campus is really nice and very green. Millsaps is another University equal distance away, but it's all fences and gates and it's not that pretty.
Jackson's downtown is also a really great place to kill time and the capital buildings are particularly enjoyable. I can suggest a few really good restaurants for both food and drinks if you're interested.
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Jackson is full of hole-in-wall places that serve prohibition style drinks. It's also the kind of place that doesn't look down on grabbing a bloody-mary before an afternoon meeting.
However, there is a helluva lot of crime, but you'd have to be deaf, dumb and blind to find it. What I mean by that, is the places you need to stay away from are OBVIOUS.