Can only comment on NYC
Go to 5pointz (large graffiti block unlike any other, professional artists)
The box - night club with wack shows.
If your into photography, NY is endless for amazing photo locations
Spoiler!
Facing NYC from Brooklyn:
If your up for a challenge, statue of liberty from the free ferry. If you know, you know how hard this pic is to get lol....
Many other locations obviously, some require alot of planning
Dont know what your transit ideas are, but i would highly suggest taking the metro everywhere you go. NYC is full of the most racist, messed up, degenerate drunks, clowns, bimbos, list is endless. I have so many awesome (and bad) memories from riding the metro.
I suggest walking one of the South bridges, awesome views.