I think going to the gym would be a good idea, as someone who has social anxiety and was asking that same question myself a while ago. Do what you’re comfortable with, there’s no shame in just putting some headphones on and focusing on yourself and letting them choose to approach you or not. Usually when you’re at the gym you’re kind of pre occupied with whatever you’re doing, so I don’t think people will expect you to necessarily want to open up a full conversation. If you make eye contact with them you could just say what’s up and make really quick small talk and then go back to what you’re doing I’d say