There isn’t much to eat directly on the Benjamin Franklin Parkway, but there is plenty within a short walk to Center City or Fairmount.
The Art Museum [1] has its own café if you find yourself hungry while inside; Darling’s Café [2] can be found behind the Franklin Institute; and the Four Seasons [3] is right there if you want to spend a lot of money.
Otherwise head south to Center City West or a few blocks north into Fairmount.
Links:
[1] http://www.moon.com/destinations/philadelphia/sights/fairmount/philadelphia-museum-art
[2] http://www.moon.com/destinations/philadelphia/restaurants/center-city-west/cafes/darling-s-cafe
[3] http://www.moon.com/destinations/philadelphia/hotels/fairmount/over-250/four-seasons