This will not be including anything that is purely for collectors (eg: pokedex, ev training and battling, shiny hunting, etc). I'm also gonna put catching legendaries and gym leader rematches as they're in all of these games
Ruby and Sapphire: Battle tower
Emerald: Battle Frontier
Fire Red and Leaf Green: Sevi Islands
Diamond and Pearl: Battle tower
Platinum: Battle frontier, the survival area and gym leader rematches
Heartgold And Soulsilver: Everything in Kanto and the Battle Frontier
Black and white: The right half of the region and find the seven sages (the battle subway can be accessed before the postgame, but some of the cares are postgame exclusives)
Black 2 and White 2: Various areas are unlocked, the Black Tower/White Treehollow (the PWT is accessible before the postgame)
X and Y: Battle Maison and looker missions
Omega Ruby and Alpha Saphire: That big island with the Battle Maison and the delta episode
Sun and Moon: Catching the Ultra Beasts and the Battle Tree.
Ultra sun and Ultra Moon: Battle tree, catching the Ultra Beasts, do the Zygarde thing where you get the key stone and the Rainbow Rocket sidequest
Sword and Shield*: Stopping Sordword and Shieldbert
*this does not include the dlc, as I think you'll be able to access it before the postgame. Once it fully releases and we know if it's postgame, I'll update this.