Awww. This was the hardest age for DS and me socially speaking and was when I showed up here too. It gets much easier. It did for us anyhow. Mainly through changing my expectations and keeping at things that showed any shred of promise.
We went regularly to a playgroup and I would spend most of my time trying to avoid DS "showing off", ie distracting him from going over to the books or changing the conversation topic, and without him knowing. When the playgroup came to my house I engineered the spread of toys to look "correct". I was so relieved when the winter platter of infectious illnesses effectively ended it.
It didn't help to try to find similar age children that shared his interests because their knowledge level was too different. Most playdates did not go well at 3 and even at 4.
But honestly he didn't need the playgroup to feel happy... I needed it, I didn't have much of a social life myself after becoming a SAHM, and really needed to meet people in my community. I was too attached to the possibility of it even beyond seeing the reality. The social connections for me happened very slowly and it ended up for me it was better to not only do things where DS was with me at the time -- for example volunteer here and there without him. It took 3 years for me to realize he just wasn't going to have a close same age friend in our community and let that go (beyond planning to move, LOL). I did find parents with either lots of kids or a disabled child of any age were far more likely to be good friend bets for me than parents with a singleton perfectly average child. Something about understanding the limits of their own power over their child's perfection. It sounds like some sort of reverse discrimination. The worst for us was parents of the excessively well groomed single child who from birth is being taught perfect manners: as a gross over-generalization the parents are invested in their child being perfect, about how their child appears to others, it keeps them up at night, they need to find inadequacies in others' children.
Our best bet socially when DS was 3 and 4 was college girl babysitters, the freshmen especially seemed to not have realized that pretend play could be considered immature, and were really energetic, they were nice to DS and appreciative of him being smart rather than feeling threatened. They loved to teach him things, he came home one day knowing the greek alphabet (sorority girl). He went to preschool part days too and that was good I think in terms of him managing in that environment, but he didn't interact much with the other kids or learn anything. At 4 he started a mixed age preschool where he was the youngest and that went better socially but was still very dependent on the particular kids.
DS now has a few interest based classes and clubs he goes to that have older kids and that's where I see him light up with social interest, suddenly completely engaged with another child. At 3 though he couldn't make it through those things without crying or otherwise being a disturbance, asking questions out of turn etc ... we tried.
We're making some effort to give DS cultural commonality. He's different enough as it is. Plus he has too many driven interests to ever turn into a TV zombie. We've done beginning soccer at 4, T ball, despite his lack of interest in all things ballish. I keep an eye out for movies to go to, try to think ahead what computer games his older friends might know about, books they would have read, etc. So that there's some common background, so he gets references and can make them himself.
Anyways, some of that is a long way off, I'm getting too far ahead. Hang in there! Look for interest based activities like library story or craft times (and check libraries further away, the closest may not be the best). Just because it says for 4 and 5 year olds doesn't mean you can't just show up, there are usually a younger sibling or two in attendance anyhow.
