Congrats on his first birthday! I think that is such a big deal for the mom, too.
For out of the house activities I would take a music class. We did Music Together but were in a different state. The rec centers offer them, there are the Gant Sisters, and I know someone local offers Kindermusik. My children both loved it, it got us out of the house, and there are numerous studies that show the benefits of music for years to come.
Other than that I remember going to the mall a lot just to let them run around in the long hallways and play on the little mall playscapes. The library is a good place, too.
For in the house my kids loved playing with water either in the tub or in the kitchen sink. Make sure you have a good, safe bench for them to stand on at the sink. That easily could take an hour. They loved bubbles and using their own plastic plates, etc. They thought they were "helping" clean the dishes.
Cheers! LA