I have been diagnosed as having AS, my partner has not (but I have my suspicions, based on how well we get along
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I found early in our relationship that I felt comfortable thinking out loud with him. I've never really worried about whether what I'm saying interests him or not. Mostly I think the subject might not be fascinating for him, but the fact that I'm into it is interesting enough (this works both ways--I'm conversant on NHL hockey, NBA basketball, audio equipment and even cars, but only because my sweetheart's enthusiasm is so infectious). Also, by doing things together (such as camping, kayaking, snowshoeing) we have shared experiences and developed shared interests, which can be the foundation for future conversations or trips, etc.
If your friend isn't one to offer up specific plans beyond 'hanging out', then maybe the two of you should try some pre-arranged spontaneity, such as walking around downtown and having dinner at the first restaurant on the left side that's under $20, or going to the movies and seeing the next movie that's starting. The anticipation can give you something to talk about, and sharing a new experience with someone can make it a little less intimidating. Good luck!