Probably not a good choice for your first cheesesteak, but for a unique take on the cheesesteak where you don't have to cross the river -
Donkey's Place in Camden New Jersey. Save on the tolls and it's like getting a cheesesteak almost for free.
My turn to rant. I suggest you avoid the Art Museum, Independence Hall and the Reading Terminal Market. All are so touristy. And if tourists go there, they can't have merit.
Tourists go to Pats but they are way outnumbered by locals. Not the preppy, foody locals, but the people who grew up in South Philly and the rest of the city. This is where generations take future generations. It is also where the cheesesteak started and, for me, at least, that makes the place a must try for any roadfooder, at least once.
I have had great cheesesteaks my past two visits to Pat's. It's taken over twenty years to do the math, but now I know the secret - hit Pat's when the line is short (not around the building) but when they are serving enough to keep the meat coming fresh off the grill. Early lunchtime is a good choice.
Geno's is good too. I prefer Pat's - more south Philly attitude, history, and they don't care what language you speak.
Tony Luke's is great. But I don't see how anyone can go to Tony Luke's and not order one of their pork sandwiches.
Getting back to tourists and I'm guilty of this too. If you don't live in Philadelphia or the burbs, you are a tourist. And if all of you non-tourist tourists keeping heading to Tony Lukes to avoid yourselves, pretty soon Tony Luke's will be so touristry you'll have to head to some place like Wawa to avoid the tourists.