I think my favorite puzzle is Test Chamber 10 (in Chapter 3), but any puzzle with Aerial Faith Plates are my favorites. I think they’re super fun.
My favorite storyline part was Wheatley’s turn to villain! In no small part due to Stephen Merchant’s acting. The moment his elated laughter slowly turned into a maniacal cackle was so well done. That moment gave me awesome chills in my first playthrough, like SHIT JUST GOT REAL OH NOOOO. :D
These are my favorite games and I’m a little sad that I didn’t get into them until over a year after the second one was released, but I love talking about them and replaying them and participating in the fandom here and there with some fanart.