Ah, I can really relate to this. We did a trial class for DD when she was about that age at the Little Gym and it was a hit. Unfortunately, we didn't have the money for it but I did get some cool ideas on things to do with her at home. For instance, sometimes I let her walk like a wheel barrow (hold her by her hips and let her walk on her hands) and now at 12 months she can occasionally do somersault.
Your DS sounds a lot like DD, especially the whole running around the room while reading books. Yet she still brings them over and has a definite opinion about what page I should be reading!

Also, I find myself nodding about the parallel play thing too. DD does a lot of pretend play and has a little doll house she plays with and wants her friends to play with that too with her. Also at the park the other day there was a 3 year old drawing with sidewalk chalk and he showed her how to draw different things and she would copy him and she was in heaven.

I have no clue where you guys live but our kids would probably do well on a playdate together.

As for what to join. We have a similar story time at the library problem. Mostly our story time is made for kids that can sit still better, which is sooooo not DD. We tried it once and she spent most of the time trying to steal the book away from the librarian so we figure we'll try again once she's older. Beyond that we go to the park A LOT and do playdates. We'd definitely do some sort of music class and/or gym class if we had the $$ but we can't afford that right now. Also what about museums? Does your city have a children's museum? That's one of DD's favorite places in the world.