In the area of Independence Mall and the other locations you mentioned are Ben Franklin's grave, Betsy Ross' house, the US Mint and the Unknown Revolutionary War Soldiers' grave. The Unknown Revolutionary Soldiers' grave is in Washington Park. If you're looking at Independence Hall, go behind it to Walnut Street and it's kitty corner to the right. When you first enter the park, there is a sycamore tree that was planted in the bicentennial year after its sapling went to the moon. It is marked as such. The grave is across the park. The park itself was a potter's field for those who died during the Revolution.
Ben Franklin's grave is to the left side of the Mall if you're looking at Independence Hall. Turn around and head towards the Mint. His grave is across the side street from the Mint and is open at it. You can pay to go inside the cemetery, but you don't have to do that to see the grave since it is right at the wall/fence. The Betsy Ross house is nearby to this, too.
You can head over to City Hall. That's the building with William Penn on top of it. It's a unique building that is quite pretty, especially if you can walk through it. IDK if this is still possible.
You can go to any of the museums. The large art museum has the statue of Rocky and the steps he ran up to the top. The Franklin Institute currently is showing Disney 100: The Exhibition.
A nice place for lunch when you're at Penn's campus is Sabrina's Cafe. It's at 227 N 34th Street. It's considered to be on Drexel's campus. It's quirky and quaint and has really good food. Make a reservation so you don't have to wait that long.
When you're in central city, you can walk through/eat in the Reading Terminal and you can also walk or drive through Society Hill. Basically, watch National Treasure and you'll get your brief tour of Philadelphia, although they run around in a way that can't be done in the timeframe that they show.
There are plenty of nice places to stay in University City, or you can stay in central city, closer to the historical places. You'll pay to park your car overnight, too. It can be $35 per day/night, so be prepared for that, too.
Where else are you planning to tour? Philadelphia is easy to get around and depending on how long you plan to actually be in the city vs. other schools, you may be better off to make day trips into it than to stay overnight. I've done both and there are pros/cons to each.
Have fun!