I've been playing Pokemon Red recently, and I noticed that to the east and west of Pallet town, there's a large field of long grass that seems as if you can catch something there. Is there a way into those areas? Or are they just there for show?

just for show unfortunately. it's kinda like the endless oceans past the buoys that you can never get into, purely to make it look more realistic I suppose

Actually it can be gotten into.
You know the dude who takes you to Brock?
If you walk down from right next to where he is using walk through walls and keep walking
You can actually get into the grassy area east of Pallet Town
If you go East from there You will find another version of Pallet Town with no people in it and you can't go into the houses
But without walk through walls, no, you can't get into there.
(I use VBA and Gameshark with a red rom)