I pretty much never go outside the random neutral stages, but...
Fox: I'll always go to Dreamland because of the high ceiling. Tons of space on this level, which is better for me than it is him. DK 64 is also a good stage vs Fox because it has a gigantic ceiling, and it's harder for Fox to waveshine you with the dips in the level (this is a minor advantage, though).
Marth: Dreamland and Battlefield, simply because they're two of my favorite stages. The only stage I hate playing Marth on is Fountain of Dreams, so any stage is fine for me.
Peach: Ban Mute City all the time, and then I'll pick Yoshi's Story and / or Battlefield. This is one of the few times I hate playing on Dreamland for obvious reasons.
Captain Falcon: It's whatever. Falcon players would probably consider Dreamland their favorite stage because of all the room, but I don't mind going there either. I've never been affected by level no matter the Falcon I've played.
Falco: One of the few times I like Fountain of Dreams, and if I like FoD here vs Falco, I'm sure this must be every Sheik's favorite stage when they play him. Besides FoD, I love Dreamland and Yoshi's Story vs him. FD isn't as impossible as people make it sound, but it's obviously last on your list.
Better players can help you more specifically, though. Take it FWIW