I was briefly a tour guide here.
When are you coming?
Anyways, the must see things are:
1) Independence Hall/Liberty Bell/Franklin Hall/etc. -- there are a bunch of old historic things that are free in what we call Old City. Franklin Hall is particularly interesting because of how bizarre and trippy it is.
2) The National Constitution Center and National Jewish History Museum are also in this neighborhood but aren't free (since they're not run by the US government). However, both are really great.
3) Reading Terminal Market -- This is at 12th and Arch and is a gigantic food court that rules. My wife and I usually eat here twice a month. It gets really crowded on weekends (especially if there's a big convention in town) but it's the best.
4) The Franklin Institute is pretty great -- especially if you have kids. It's on Ben Franklin Parkway which also has The Rocky Statue. And the Art Museum behind the Rocky Statue is pretty awesome.
5) Right by here in the Fairmount neighborhood is Eastern State Prison, which was the world's first penetientiary. This is probably my favorite museum in Philly. They get about a hundred requests per year from death metal bands who want to record a video in there, if that helps explain the atmosphere.
6) The Mutter Museum is this awesome medical oddities museum with horrific medical devices from years gone by.
I'll tell more later.