There's a few places I'd recommend. I live in Durham now so haven't been down in Raleigh for a couple of years so things may have changed since then.
1) There are a couple of BBQ places downtown that you should check out. Some say The Pit, some say Clyde Coopers.
2) Ashley Christensen is a renowned chef who has a couple of places downtown. Either Poole's diner or Beasleys Chicken and Honey are good choices downtown for food. A 3rd one is Death and Taxes, but I've never been to it.
3) Brewery Bhavana and Bida Banda (Laotian food) are two very popular places with the same ownership group, but sometimes hard to get a reservation on short notice. Brewery Bhavana is a weird concept but kind of cool. It's a dim sum restaurant, a book store, a florist and a brewery all in one. I like both places.
4) There are a couple of food halls (Morgan Street Food Hall and Transfer Co. Food Hall) where you can try multiple different things. I haven't been to either one.
5) Over on Glenwood is the worlds largest beer garden (Raleigh Beer Garden) with over 350 beers on tap. The Flying Saucer off of Morgan and Harrington would be another good option. Clouds brewing is over that way as well. It's one of those "pour your own" places.
6) If Pizza is your thing, Trophy Brewing has great pizza but it's probably 1-1.5 miles from downtown so not too far, but probably best to Uber.
7) If you want Vegitarian/Vegan food, then Fiction Kitchen is fabulous.
8) For Breakfast, many people like Big Eds City Market. I haven't been there in about 5 years though.
I don't know of many "must see" historical things downtown. There's a history museum and science museum, but those aren't "must see" in my book. Probably one of the most historical places is Krispy Kreme donuts over off Peace and Pearson street.