Affiliated with nearby Drexel University, the Academy of Natural Sciences is right on the Ben Franklin Parkway, near the Franklin Institute and not too far from the Barnes Foundation and Rodin Museum. If you like dinosaurs, they have over 30 species represented, about half of which are full skeletal mounts. They also have dinosaur eggs, footprints, etc.
They have rotating exhibits, so if the natural sciences are your thing, check it out!
The Franklin Institute is named after the American scientist and statesman, Benjamin Franklin. Located on the Benjamin Franklin Parkway, it was founded in 1824, making it one of the oldest centers of science education in the U.S.
There are too many science exhibits to describe, but one of the most famous is the giant human heart exhibit so big you can walk through it. There are exhibits on electricity (a nod to Ben Franklin's kite experiment), trains, sports, and more. There is also an IMAX theater for those interested, a planetarium, and rotating exhibits that can be quite amazing. It is not just a place for kids--you will often see adults on their own, and they even occasionally have happy hours aimed at young adults called "Science After Hours".
The Franklin Institute is definitely a unique and fun experience.
Although it is not in the nicest of neighborhoods, the Philadelphia Zoo itself is very nice indeed. While some other cities in the United States had collections of animals on display to the public before the Philadelphia Zoo opened, the Philadelphia Zoo lays claim to being America's first zoo. I have not gone since my children were young, but I have fond memories of the place. It is far from Center City, so don't even think about walking. Take an Uber or cab instead.
Formerly the Chemical Heritage Foundation, the Science History Institute is home to an impressive and free exhibition on the history of chemistry. It is a stone's throw from Amada, so grab a bite to eat there before or after.
Anyhow, they also have a wonderful collection of art depicting alchemy as well as books and other artifacts related to the history of chemistry. The name was changed to the Science History Institute from the Chemical Heritage Foundation when the latter merged with the Life Sciences Foundation. As a chemist, I preferred the old name. That aside, it is a great place to visit if you are even remotely interested in chemistry and science.