I would not be in ANY major city right now (post-2020 really) without a concealed carry. As a former travel agent, I highly recommend contacting your airline beforehand to double-check their particular rules (avoid surprises at the airport!) Here is AA as an example:
https://www.aa.com/i18n/travel-info/baggage/firearms-and-ammunition.jsp#:~:text=and ticket changes-,Requirements,traveling with firearms and ammunition
In general, your firearm must be unloaded and, in a TSA approved, locked case. Ammo should be in a separate similarly approved and locked case. Your firearm will stay with your other checked baggage until you reach your destination (it will just briefly see the light of day in gun-free Chi-town as the baggage handler stows it in the next cargo hold). Then, you will most likely need to claim your "special baggage" at the customer service or "lost luggage" counter. It is a process and a bit of a pain, but if you have reciprocity then better to have it and not need it... In Philly unless you have to go into a secure area with metal detectors, carry wherever you
legally can and/or just abide by the adage: "better to be judged by 12, than carried by 6!" Other than all that, enjoy some history and cheesesteaks!
P.s. If you are going with other adults, carry in a fanny pack. When you get to a secure area like Independence Hall where there will likely be metal detectors, take turns doing the tour/ being keeper of the CCW. As long as you just look as touristy as possible, no one will think anything of it.