For the first couple of dates, people recommend not going to a movie because you don't really interact with each other. Something that makes an impression like miniature golf or go-carts or a nature walk would be appropriate. Just don't pick something that's out of your price range; be realistic so you don't set unrealistic expectations. You can always go out for coffee or something if you prefer not having an actual outing.
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many ASD traits - not formally diagnosed