J: Hey, Crown. Do you Wanna hang out tonight?
C: Um, I can’t. I have to go home and do laundry. So I’ll be hanging out laundry.
J: Okay, what about this weekend? We can go for a picnic.

⇑Why they use "go for a picnic" not " go on a picnic"?

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"We can go for a picnic" sounds so natural in this conversation. I'm trying to figure out why.

I think because he says "We can go" instead of "Let's go." That's a short way to say "We can go out for" which is a very natural phrase.

Either "for" or "on" works fine here, but in this context, "We can go on a picnic" might make me laugh. It's hard to explain why, but it would sound like he's jumping to a conclusion instead of just suggesting a possibility. It's unexpected. Almost like, "We can go to the circus!" Like he's suggesting a really unusual thing to do without explaining why he thought of it.

"We can go for a picnic" sounds like he's suggesting just one possible thing they could do, but they could do something else instead. It's less enthusiastic.

By the way, most people in the US use clothes dryers instead of clotheslines, so they wouldn't say, "So I'll be hanging out laundry." They would be more likely to say, "So I'll be folding laundry." However, first generation Chinese-Americans usually do use clotheslines. So it depends on who is speaking.