Camden is across the Delaware River in New Jersey and not worth a visit unless you are going to the NJ Aquarium IMHO. Put it this way, no one goes to Philly to see Camden (Don't mention "visiting" Camden to anyone in Philly because they will die laughing.)

For 1st visit, stick to Philly "Center City" (downtown shopping! restaurants! skyscrapers!) & Independence Mall area (History! More Museums!) OR Logan Circle -(Arts! Sciences!) Museum District. Go to the top of City Hall -beautiful building -If open. Seems the tower observation deck at Liberty Place (skyscraper) is closed permanently. Too bad.

That's more than enough for a day trip. Decide which museums you want to see and stick to those because $$$. (You aren't in DC anymore no more free museums!) Indep Hall and Logan Circle are in two totally diff parts of the city so keep that in mind. The Museum of Fine Arts is HUGE also keep that in mind. The Natural History Museum and Franklin Institute (with its famous walk through heart!) are great too if you are into those subjects. Southie which is in Boston is similar to Camden in that no one goes to Boston just to go to Southie which is mostly residential though there are museums on the waterfront edges, which might technically not be in S. Boston, but somebody can check me there.

Also would not try to do Philly and NYC in one day. Again IMHO Toooo much. Def different trips. Why rush? You would spend more time on bus/train than in either.

Also whatever you do if you take Amtrak, get your ticket 14 days in advance. As you get closer to the date you want to go the more expensive tickets get. Also might be good to sign up for Guest Rewards and earn points for *free* future travel. As for bus would never take it to NYC because traffic on NJ Turnpike is no joke. It is almost 24/7/365. YMMV. If you must bus, leave as late or as early as possible because traffic. If you like to sit in traffic, well...OK have plenty of things to do/read/watch/snacks/sandwiches etc.