Walnut Street is a tow-away zone from 4:00-6:00 pm!
If you arrive after 6:00, you're generally going to pay about $2 in quarters to park at a meter. There's two hour parking until 8:00 PM on almost all of the side streets: 33rd Street, 38th Street, Walnut, Chestnut Street, 34th Street between Walnut and Chestnut, South Side of Spruce, and places further out.
If you arrive before 6:00 PM and you don't want to circle until 6:00, you can either park somewhere other than the north side of Walnut street (you will be towed on Walnut) and be sure you keep the meter fed until 8:00, or else seek out meters with 3 hour parking until 8:00 pm. (I believe 34th street between Chestnut and Walnut is that way, and I think 37th street also between Chestnut and Walnut is that way, and maybe 33rd street)
38th Street north of Market is a little far, but it is always free, and almost always available.
Above all, just be sure to read the signs (carefully). Philadelphia is full of places that have spaces where you can park for free during a restricted time period, but have no "green" in the sign indicating you might be able to park there. Conversely, parking tickets arrive quickly and fines are steep.