On Mother 1 it's definitely the whole last part, starting from Teddy's town (Ellay or Valentine). Getting into the night club, having a drink and go to jail. It's one of the biggest clichés in RPGs, when you get captured and you lose all your items. But the way it's done here has the parody and humorous element that makes it so memorable. You just buy your equipment back from the same policeman after you get free. Police officers selling weapons to kids, great.
Then the whole Teddy scene when he fights you, then joins you, and kicks Lloyd out for being a nerd. He comes off as an asshole, but then you learn about what happened with his parents and his motivations and you feel sympathy for the guy, plus he's a great party member with lots of buffed stats to tank through the perilous cave to reach the final destination of the game, Mt. Itoi. I won't narrate the whole Mt. Itoi sequence, but damn the plot advances a lot and it's all done in beautiful 8-bit sprite and sound aesthetics.
For Mother 2 I really like the beginning, Onett feels super nice to stroll through, and dealing with gang members and Frank was a nice nod to Teddy and his gang on M1. Then of course Fourside/Moonside, Saturn Valley.
On Mother 3 it's when time passes and you see the transformed, urbanized Tazmily Village, chapter 4 I think. Lots of stuff going on, you just need to talk to everyone to learn what happened. Also Tane Tane Island.
Favorite NPC is the moms in all 3.