Things like swimming, arcades, trains, buses and cable cars can all be part of an EOTIC package. DS3 went on a steam train last week. DS1&3 both go swimming.
I know a young man who is ticking off train stations across the country. He and his tutor choose a station, look at it on a map, plan the route, buy tickets, travel, take a photograph of the station sign, send it via WhatsApp to family with a short message, go for lunch/cake/drink/whatever, then travel home. They print a photograph of the station sign, stick it in a scrapbook (sometimes with a couple of words underneath) and finish by ticking the station off. It covers numeracy, literacy, IT, geography, PfA and so much more. For stations further away, they have combined the education hours and the social care PA hours/activity budget to stay overnight.
I appreciate why you are avoiding them, but just so you know, theme parks can be funded too.