Brinstar is the most fair I think. Mute City's lack of platforms really hurts everybody that can't recover very well and helps those whose main gameplan centers edgeguarding (ehem, Fox Falco Sheik Puff Marth) while still having a damaging floor at times (like Brinstar). Pokefloats is a joke that need never be discussed. I think when you look at the stages closely, the differences between them are so distinct it's amazing that we even need to discuss this:
Legal: You can't mess these up, honestly
Battlefield (Truest neutral stage; even the Battlefield'd element is negligent given other opportunities it offers)
Dreamland 64 (Wispy upsets a lot of the balance here, but it genuinely is better than Battlefield aside)
Fountain of Dreams (Why exactly is this stage so bad? Random platforms are far better than a lot of things)
Yoshi's Story (Tiny blast zones are rough and Shy Guys occasionally interrupt the flow of a combo)
Final Destination (The lack of platforms opens the doors for chain grabs and tech chases for days)
Pokemon Stadium (Transformations suck, but its default is the best platform arrangement in the game)
Almost Counterpick: In good company with a solid attitude, these can be fair
Jungle Japes (The most dramatic problem is the klaptraps. Not much else is too horrible here)
Kongo Jungle (Kinda like WarioWare with better blastzones. The side rock is an issue, though)
Brinstar (The acid is severely limiting at times, but helpful at others. Platform design is solid)
Kongo Jungle 64 (About as large as Dreamland, but could allow for circle camping with the high platforms)
Mute City (Lack of grabbable edges, damaging floor, and set-pattern hazards aside, it's a decent stage)
Great Bay (Spacies do well to circle camp this stage)
Casually Acceptable: When you're a few brews deep, these start to be a good idea
Rainbow Cruise (I will back this stage to no end, but understand fully how obnoxious it gets)
Onett (Walk-offs...)
Yoshi's Island 64 (It's a tad too large and cloud camping is viable for a moderate amount of time)
Brinstar Depths (I could honestly see some worth in this stage, but I'd need to play it more to see how it works)
Princess Peach's Castle (The walls kinda kill it, but otherwise it's one of the most balanced in this group)
Green Greens (The close blast zones are ridiculous and the bombs are troubling and allow for unbalanced play)
Big Blue (As far as mobile stages go, this is the most acceptable)
Fourside (the pits only REALLY hurt Ness, and so long as nobody wall-jump camps, it's an interesting stage)
Venom (The walls are tricky, and the sloped platforms make playing difficult for some)
Corneria (That low ceiling? That wall? Arwing hazards? Yeah no)
Yoshi's Island (Walk off sloped edge? Fox has a field day here. That's even before the breakable floor)
Mushroom Kingdom II (The walk-off edges are bad, Birdo's bad, but the center area is lovely)
No: Literally would refuse to play if this came up
Mushroom Kingdom (The walk-off is a huge issue here, along with the dumb-as-hell block gimmick)
Temple (It's big and dumb)
Flatzone (It's tiny and dumb)
Icicle Mountain (It's boring and dumb)
Poke Floats (It's just dumb)
I like a lot of stages that are banned, but there's no reason to bring them into the mix; I never get bored playing the 5 and a half legal stages we have already. We certainly COULD expand the list and give more bans to make this a thing, but just look at how Project M tournaments run right now compared to how succinct and fluid Melee is.