When my son was little there was an early childhood music educaton program at TCU. We started him when he was quite young. Similar programs are Kindermusik and Musicgarten. There are several around in the area, but I'm not sure where. First United Methodist Church in Grapevine is probably one of them. The Master's Touch in G'vine. Seems like one of the rec centers has it also.
Check with the recreation centers for other activities also. You usually don't have to be a resident to sign up, so check the neighboring areas as well.
Another thing is swimming. Several places around have a "mom and me" type class. Probably Emmler is closest to you, but the Keller Pointe may have one also.