A big part of watching MLB playoffs for me is the ambiance of it all. Certain stadiums have a great ambiance and sort of lend to an "epic" feel. The games feel more weighty and important. For me it's less about the history of the stadium than it is about the "feel" of the stadium. It's always a bummer for me when the World Series is played in a crappy stadium.
This year the 4 teams remaining all have good ambiance in their stadiums IMO!! (Angels, Tigers, and Nationals DO NOT, so I'm glad they are out)
Orioles Stadium has a sort of old timey feel to it, especially in right field.
Royals stadium doesnt have tradition on their side, but it is a cool stadium and the crowd is awesome.
Cardinals stadium SCREAMS October, and has one of the coolest views from home plate in all of baseball. (Seen it with my eyeballs tbh)
Giants have one of the best ballparks in MLB, right on the water in teh bay area.
ALCS and NLCS will both be rad, and the World Series gonna be off the hook bros.
Hoping for a Royals vs Cards Show Me State Showdown, but would be cool with the Giants advancing cuz I might be able to make it to a WS game (living 3 hours away from SF).
I love the Orioles Stadium with the bricks behind home plate.. really has that old time feel to it like you said.