Hi S.,
I will echo two of the activities previously suggested -- the two I know more about. KinderMusic (Google for locations) and the YMCA. The Abington Y is a nice facility; there is also a Y in Northeast Philadelphia. If you join one Y you can participate in activities in the other -- there's reciprocal arrangements for many Y's in the area. The Northeast Y has swimming classes for mommy and me as well as other offerings. The Northeasy Y (and possibly the Abington Y) have babysitting so you can go to the gym, swim, take a fitness class, etc. (you just need to be in the Y while your child is in babysitting). They are online as well.
The Please Touch Museum, while not an ongoing activity, is also a lot of fun and discovery for kids from 1 to 7. You many want to consider a membership so you can go as many times as you want. One year olds don't usually have the longest attention spans : )
You can also take your son on walks through a park. There are often many things to see there. One year olds think everything is new. I know of Pennypack Park in Northeast Philadelphia and Wissahickon Park in Chestnut Hill. Not sure where you live, but there are a few parks around the city that are fairly easy to get to.
One can be such fun, and it only gets better. Enjoy.
S.