Moerlein Lager House in the Banks near the ballpark recently opened and I've heard a lot of good things about it. Christian Moerlein is a local microbrewery, so you could sample their beers and get food at the same place.
Montgomery Inn is the famous local rib place and many people like it a lot. I have honestly never seen the attraction, even when I was a meat eater. But as I said, lots of folks swear by it. They have a couple locations, including one on the riverfront not too far from the ballpark.
For Cincinnati chili, I like Skyline, but I'm sure others will have strong opinions on this.
Hofbrauhaus in Newport is a fun place to go for food and beer before a Reds game. Can easily take the Southbank Shuttle across to the ball game from there. Unfortunately, I don't think they had goetta on the menu anymore the last time I was there. Goetta is a local delicacy, a sausage with oats. It is one of the foods that makes me reconsider my commitment to vegetarianism. There are a couple stands at GABP that sell Goetta dogs.
Graeter's is the famous local ice cream store, and they have locations around the city. Although as a native of Oakley, I have to put in my plug for Aglamesis Brothers as superior to Graeter's. Their ice cream parlor is unchanged in decades and is on Oakley Square. I think they still have another location in Montgomery, too.
Beside Moerlein, Rivertown and Mt. Carmel brewing are a couple of newer local micros that put out good beers. The Hudepohl brand name has recently been revived as well. It was the big local brewer for years. Beers are closer to big macrobrews like Bud or Miller than IPAs or other craft beer styles, but a Hudy Delight or Little Kings is part of an authentic Cincinnati experience! You can buy Hudy at GABP in the little United Dairy Farmers stores.
Are you looking for any particular sport equipment? Dick's Sporting Goods is the dominant chain big box sports store. There are several around the city. Koch's Sporting Goods downtown is a local store and was always good when I was younger, although I haven't been in there in probably twenty years. There is an REI (similar to MEC in Canada) opening at Rookwood Commons this summer, but I think it won't be open until July. If you're looking for fishing and hunting gear, there is a Bass Pro Shop in Forest Park.
There are a couple large flea markets off I-75 in Monroe, about 20 miles north of the city. Trader's World and Turtle Creek. Although I think they have mostly newer stuff. There's a similar large flea market off I-71 about 40 miles north of town at Caesar Creek. There's also a big flea market in Richwood, KY, about 20 minutes south of the city.
Waynesville, Ohio, which is in Warren County about 30 miles NE of the city, is known for antique shopping. Springfield, Ohio, which is about 20 minutes east of Dayton on I-70 has several huge antique malls right off the highway.