<--- has lived and worked in Philadelphia since the 1990s.
I'll second the recommendation for Dinic's, specificaly the roast pork sandwich with either broccoli rabe or spinach. It's a classic Philly sandwich that is hard to find (at that level of quality) in many other places, although John's Roast Pork in South Philly will give it a run for its money. I heard you can get pork cracklins on top of the sandwich as well so ask for it -- even other Dinic's locations (e.g. the one at the Philadelphia Navy Yard) don't offer cracklins.
I suppose the Philly cheesesteak should be on the list as well, although the best steak place in Reading Terminal was evicted many years ago (Steve's Prince of Steaks). Personally I would go for the pork sandwich from Dinic's instead. If you want a cheesesteak in Center City then get one at Jim's near 3rd and South Street. (Yes, there are better cheesesteaks in the city but we are talking about Center City here.)
If you are into (or just want to try) Amish cuisine (I grew up 30 mins from Lancaster), I also recommend getting breakfast at the Dutch Eating Place. It will be crowded so get there early if you want a seat. Local specialties include the chicken pot pie (note: if you've not had it in this fashion, there is no "crust", only noodles) and shoo fly pie (this is not as sweet as it sounds, this is why they serve it with whipped cream).
I do NOT recommend getting breakfast at the Down Home Diner in Reading Terminal. Honestly I'm not sure why they have such a following. The food is subpar. Go for the Amish Eating Place instead.
I also think Beiler's bakery has the best donuts in the city. I know people here crow about Federal Donuts but I've had a few and they seem overpriced and overhyped. If you want a classic Philly dessert, try Termini's cannoli (also available at Reading Terminal).
Note: Beiler's and the Dutch Eating Place (and the other Amish stores) are not always open. As an example, I believe they are not open Sunday (even though the rest of the Market may be open).
For other sights in/around Center City I would recommend touring the USS Olympia (the last surviving warship from the Spanish-American War) if you're into military stuff. The museum has been having constant trouble maintaining her and I suspect they will run out of money soon and scrap her. We will lose the last ship of her kind when that happens. Otherwise I'd recommend the usual historical sites -- Independence Hall and the Liberty Bell.
Keep your head on a swivel. There have been multiple shootings/stabbings in the best parts of Center City over the last few months (the last shooting was near Rittenhouse Square last week, although at 2 AM). It used to be that Center City was basically "safe" (as much as a big city could be) but with the events of 2020 it is no longer the case. Philly now blames its ever-escalating crime problem on "gun violence", instead of looking hard at the lax (or non) enforcement of laws. The broken window theory is rapidly making the best parts of Philadelphia dangerous and I fear we have started to see all the progress from the late 1990s unwind.
PS is there a specific Turkey Hill you are visiting or are you going just for the ultra-sweet iced tea in any one of their gas station locations?