Oh boy. That's a fun question. So many choices.
For fast food, 0bviously try Bojangles if you haven't had it before. The Cajun Filet Biscuit Combo is a little slice of heaven on earth. Just make sure to get unsweet tea.
If you do go drinking, hitting up Cookout after is basically a rite of passage. A cookout tray will provide you with all sorts of food and a fantastic milkshake for like $6. Waffle House is also acceptable, but tends to be significantly more sketchy.
There's also a local chain called Guasaca which sells arepas, which are basically pancakes that are sliced open and filled with meat. They are quite delicious.
For a real sit-down meal, I'd check out Caffe Luna which is a fantastic little Italian place downtown or Relish, which is a bit to the north, and has a pretty wide range of food and drink, plus their have a constantly rotating test menu that always has something fun on it.
There's also a local legend called Player's Retreat, and while I've never actually eaten there, I've heard it's amazing. They grind their own beef in house so it's possible to order a burger rare
As far as wetting you whistle, we've got a World of Beer and a Yard House, but I'd skip those and hit the Raleigh Beer Garden if possible. They have a ludicrous selection of beer. Just look at it:
Raleigh Beer Garden: Beer Menu
The Flying Saucer is also a fun place to check out.
My personal favorite sports bar is called the Brickhouse, although I haven't been in ages due to Covid.
I haven't been since it just opened, but I feel like you're pretty obligated to go to Bates Battaglia's new bar, Teets, which I think I mentioned here.
Boxcar is a barcade which is a lot of fun.
Of course, the crown jewel of food in the area is the Angus Barn. It's truly an experience. On top of their dining rooms, they have a lounge for eating/drinking and a lounge for smoking cigars. It's a bit on the expensive side, but holy hell is it worth it. They do a fantastic job of balancing being upscale and homey. I cannot recommend it enough.