Here are my personal opinions, and the way I usually counterpick is based on this...
This includes disadvantages too...
DK and Fox have big advantages on Hyrule and should fight there as much as possible. It's also Link's best stage as he doesn't die as easily. Falcon generally has an advantage there except vs. Fox.
Dreamland is an excellent anti-Fox level since it's really easy to just throw him off and edgeguard, and platforms can get you around his lasers.
Peach's Castle is good against any character with limited recovery options, like Samus, Mario, and Luigi, as they often get screwed trying to recover when the only option is going to the bottom moving platform. However, Samus is also tricky with platform-drop aerials on that stage.
I think that Congo Jungle is an excellent Kirby level as he can use the central platforms to prolong his drill up-tilt combos, then finish with a smash really easily, as the platforms are too small to escape with a tech-roll. Kirby can also use the barrel more easily than other characters and can recover through the floor to save himself in situations where he would be too predictable to recover safely. He also can get really fast kills there since the borders are really close to the stage.
I think that Congo Jungle is also a good Samus level since the kick KOs really fast there and she can pull off a lot of neat stuff on the platforms. Samus also performs well on Hyrule as long as you aren't facing Fox or Luigi (vertical KOs), as she never dies and can often get 175%+ on a stock.
Ness fails on Saffron City for obvious reasons.
Mario performs very well on Dreamland provided the player can edgeguard well. It's also Pikachu's best stage if the player can do those Uair off the stage death combos. Pikachu should also always pick Dreamland vs. Samus, Mario, and Luigi, as it's like impossible to avoid the f-smash edgeguard.
That about covers it as for what I know...