Suggestions:
Watch some of the DNC protests going on. Some pot activists marched miles down Broad street holding a fourty foot inflatable joint on Monday.
Definitely go to Nocturnal. People say Exit is cool too, but I stick with nocturnal, and it's closer to a lot of other stuff you'll probably want to check out as well.
Go like a block down and get a cheesesteak at Jim's. I like that place better than Pats or Genos.
Go some more blocks West, get some pot from the rasta head shop, and go to the Magic Gardens.
https://en.m.wikipedia.org/wiki/Philadelphia%27s_Magic_GardensA bunch of historical sites (Liberty Bell, Independence Hall) are located a little North of Nocturnal.
Love is dead, but you can still skate at the Municipal building.
The art museum is definitely worth checking out if you have the time. The Barne's museum is also by there. Paine's park is located close by as well.
Go to FDR.
There's a ton of cops out right now for the convention, which may or may not be helpful, depending on where you're trying to skate.
I just noticed you said you're not bringing a board, so ignore the skate stuff