I live in Macon, only been here 2.5yrs tho so hardly the expert.
The Rookery in downtown is probably 'the' restaurant to check out on your first visit, assuming you want a burger. My understanding is they were the first that started the revitalization of downtown. I like the Johnny Jenkins (sweet and sour pickles and pimento cheese) and the Jimmy Carter (peanut butter and bacon!). The milk shakes are good but pretty expensive IMO for the size.
Dovetail is upstairs above the Rookery, and is REALLY good but a little spendy. We go there for special occasions now and again. My advice is get an appetizer (the put ups are awesome, they have a bacon spread thats crazy good) and a 'small plate'. Save you some money. And if you're still hungry go get a shake downstairs or ice cream a door or two down the street (I think the place is called Scoops).
Kudzu seafood has banging shrimp po-boys.
There's two "new" breweries, Piedmont and Ocmulgee. Both have okay food, lotsa beer if you're into that (I personally don't drink so can't comment much beyond that). One of them has a little game room downstairs, but I can't remember which one, I always get the two mixed up and haven't been to either much.
Several other good places to eat downtown. Most places downtown are good actually, it's hard to go wrong. For more upscale (besides Dovetail) look into the Tic Toc Room (rack of lamb is on point) or Downtown Grill(e?) (I haven't been there yet but hear it's great).
If you want pizza, just a few miles outside of downtown is Ingleside Village Pizza, it's good.
If you need other stuff to do, The Big House is where the Allman Brothers lived when they got their start here in Macon, it's worth checking out. You could even visit Rose Hill cemetery and see Duane and Gregg's grave. Just across the river from downtown is the Ocmulgee Mounds, they've found artifacts going back 17,000 years. It's was the largest archaeological dig in US history.