1) Not just Fairmount Park, either. Try the "John Heinz Wildlife Preserve," better known to its friends as Tinicum -- the only major wildlife preserve within a city, it is said. Great place for butterflies --
On the other hand the Wissahicon branch of Fairmount has its own covered bridge. Not something you will find in other big cities.
http://william-king.www.drexel.edu/top/bridge/CBTmill.html2) Don't rule out the suburbs -- even if you are a big city guy -- Philly has some very cool old suburbs. A friend of my wife's, small town girl more or less married to a dog (human males didn't work out) found Northern Liberties, an urban redevelopment area, a bit too much of a raw urban experience -- but conversely several of my younger colleagues have found Jenkintown a great price-amenities compromise. Jenkintown is to the north of Philly, but has excellent rail connections to Center City. Say what you will about SEPTA, and a lot of bad things are said, it is still a Philly asset! Jenkintown is also convenient to the Keswick Theater, whch is great if you are into jazz and old-time.
3) And hey, Yo! We ain't stuck-up like dose San Francisco hotshots -- we say Philly. She's our town, and we love her, so we call her by her nickname.