When I lived in Philly my apartment wasn't in Center City (downtown) but I did walk around a lot there and I can vouch for each of these places as excellent reading spots along with being good outdoor hang-outs; some of them are crowded and lively, while others are quiet and out of the way.
People often raise safety concerns about Philly, but I never felt unsafe in any of the places listed below (mostly because I visited them in the daytime, usually on Sunday afternoons); in any case, use your common sense and listen to your instincts if you feel uncomfortable anywhere.
Click on the name of each place for a link that will give you more information about location, history, and what you'll find there.
Rittenhouse Square
Washington Square
Magnolia Tribute Garden and Rose Garden (they're across the street from each other)
Penn's Landing
Schuylkill Banks
Swann Memorial Fountain at Logan Square
Mütter Museum Medicinal Garden
(Hmmm... at the link it says this garden closed today to the public "so that we may preserve our National Historic Landmark Building." No word on when (if?) it will reopen. The museum is still worth visiting, if you're interested in medical maladies and oddities and don't get too squicked by the sight of fetuses preserved in jars.)
Race Street Pier
Like Penn's Landing (see above) this is also on the Delaware River.
Signers Park
18th Century Garden
Because the Mütter Museum garden is closed I'll throw in a bonus suggestion:
The Art Museum's "Rocky" steps
If you don't mind people racing past you in imitation of Rocky.
Some of them look the part, too.
