Not sure what area you are looking for, but Huntington Beach Adult School has this. (Other school districts probably also have them and Coastline community college has one). I know the one in HB is very school-like, but you attend with the child. They have different classes for different ages. It is very inexpensive. It is treated like a class for you (is considered a "parent eduction" class and you have to do some kind of self-paced assignments). http://www.hbadultschool.com/Par_Ed_classes.htm
You can also take classes through your city. HB's info is at: http://www.huntingtonbeachca.gov/Residents/news_publicati...
As for the interaction aspect, I highly recommend joining MOMS Club (www.momsclub.org to find the club for your zip code). A weekly playgroup is great for interacting with other kids and they also have lots of other activities (i.e. opportunities to interact with other kids) during the month. The annual dues are cheap compared to paying for private classes/activities. My Gym is great, too; it is pricey, but a good deal if you take full advantage of the Free Play sessions in addition to your assigned class (http://www.my-gym.com). You could also go to the park, where there are always other kids. Your child is young, so he will not really be playing "with" other kids for quite some time, but I certainly understand you wanting to give him opportunities to interact.