Is to sleep in (wink, wink).
Go to the Natural Science Museum at LeFleu's Bluff State Park. It sounds lame, but they have a lot of aquariums and is actually a really cool place. Best museum in Jackson by far.
Breakfast- Broad Street Deli/Primo's- grits!
Lunch- Keifer's/ Rooster's/Stamp's
Dinner- My personal favorite is the Mayflower. It's kind of like Medival Times Mississippi style because you can watch the waitresses beat up the homeless people that ask their customers for money and stuff like that. Make sure you sit FACING the street. It is a little pricey. You also will feel like you might die because you have to park in a dark alley, but somehow it's all good. Everytime I take a girl there, at first they are like- "Do you know where you are going?" but afterwards they want to go back again. They have great seafood. I go for the seafood platter, but I'm a glutton.
Now, since you are going to the game, you will probably want to go somewhere quick. You can eat at the ballpark, but of course it is pricey and it's not worth what they are charging. Unless you want to pay 12 bucks to give yourself gas for some reason. Traffic is probably going to be bad, so I recommend going at least an hour and a half if you want to watch the first pitch. There are some restaurants around Trustmark Park, mainly (all) chains ranging from Cracker Barrel to Wendy's. I would probably just do that if I were you.
Also- the Mississippi Sports HOF and Museum is pretty good to. It's right across the street from LeFleur's Bluff State Park and also, the Agriculture Museum is pretty good. Your girlfriend would probably like the Fondren District. There are a lot of little shops and things like that there. Parking sucks, though.