There is a hop on/hop off bus tour throughout the Center City/Historic Philadelphia area - it's a very historical area for us over here. The Liberty Bell has just been moved to its own area, Betsy Ross House, Ben Franklin, Constitution of US, etc. There are many volunteers that get dressed up in costume, etc. and talk about what life was like when our constitution was being written Depending upon your daughter's liking, it could be interesting. I liked walking through the old houses.
Penn's Landing (by the Delaware River) is a nice area to walk around in and there's usually always something going on over the weekends - though may not be to a 13 y.o. liking.
You can walk over to South Street from Penn's Landing (must walk over bridge that's over very busy Route 95 road, but SAFE.) South Street has a lot of "cool" shops & gets very busy on the weekends. My 14 y.o. & I like to walk up & down the street just looking at some of the people. They look weird, but from my experience, everyone has been extremely polite & nice, just, well weird looking.
I agree about the beach!! Her guide family will fill her in about which one they're closest to. She will need a beach tag (every beach requires one, except for Wildwood - I think), but tags can be bought on a daily basis and are sold by teenagers walking around on the sand. The water may still be a bit cool in July, but it all depends on what you're used to - rent a boogie board!! Great fun!! My son's favorite thing to get at the beach is a "Fudgie Wudgie" which is just a frozen chocolate pop. These guys carry ice chests around (can you imagine?) and you can get a frozen treat in the high heat of the summer.
Just warn your daughter about the seagulls - they'll steal your food right out of your hands if you're not careful! They've just gotten horrible.
I second the opinion on Six Flags; however, there is a water park there - Wild Water & a drive through "safari" which just doesn't compare to AK. I've never been to the water park since I've been spoiled by WDW, but it would be something different for your daughter since it's here, I guess.
Baltimore's Inner Harbor has a fantastic and very popular aquarium. It's beautiful there. It's about a 2 or 2.5 hour trip south, depending where you are in NJ.
NYC isn't too far - again, depending where she will be in NJ, I'd say about a 2 or 2.5 hour trip north. I've only gone into NYC about 3 times and always near Broadway. Can't tell you too much about that City except there are wonderful places to shop!!
That's all I can think of right now - pls. feel free to PM me if you have any other questions.
Your daughter will have a blast!!
Jane