To a point, Josuke's entire existence sort of makes Jotaro feel weird. It's an uncle, younger than him (though not by much, here), who he never knew existed... and who's the result of his grandfather cheating on his grandmother. But that's not Josuke's fault, he knows, so it's unfair to hold it against him.

As far as Josuke himself, Jotaro's found him really pleasant. He's kind of a dork and a little immature, but really, he's a more tolerable Joseph.