Used to live south of there (York) a few years ago. Harrisburg is just your average small city, nothing special. Seldom went there so don't have great recs right in the city itself.
Carlisle is just west of there, used to go to a good bar (great beer selection and very good food) called Market Cross Pub right on Hanover St.
A few miles east of Harrisburg is Hershey. Cute little town. Some good restaurants. There is a great brewery called Troeg's. Large, nice brewery, very open so can be a bit loud if crowded, decent food, and good/great beer. Also at Hershey Park, the amusement park, there is an arena where the Hershey Bears play a pretty good level of hockey.
30 minutes south of H'burg is York, not much going on there. There is a Harley Davidson factory where they make the Soft Tails, but I think the factory tours are temporarily closed. One of my all time favorite breweries is there, South County. They do IPA's very well! A beautiful post and beam building, great beer, good food, pinball machines.
A bit to the southwest of H'burg is Gettysburg. Depending on weather, a guided tour of the battlefields is fantastic, but even just driving through and a little walk can be really interesting. There are also Civil War museums around.
Be careful driving. PA drivers are garbage. There is no hands-free law so everyone is on their cell phones while driving, they don't keep right on interstates, and drive two speeds....way too slow, or way too fast.