The only advantages I'd give Pit here are platforms and the fact that he can attack through the floor (very helpful) when the stage is moving. Everywhere else, though? Nothing messes with him too much, but it certainly doesn't play to his strengths. Platforms are rare on the ground. I think the umbrellas are the only ones. Water and walkoff edges eliminate the advantages of his strong recovery and gimping abilities, and since his spike can only be performed on solid ground he can't "dunk" people like many other characters can.
Personally I'd never counterpick this stage as Pit-- Halberd has all the same advantages without the walkoffs or water-- and it'd be one of my lower priorities in stage strikes. I'd rather play on Delfino than PS1 or Yoshi's, but BF, Lylat, and Halberd are all much better.
Edit: Seeing as I kinda missed this thread for a while, I'll add my thoughts on the previously discussed stages.
FD: All in all I'd consider it mostly "meh" for Pit. Pit likes platforms because of his SH aerials and the tech-chasing abilities they grant. Plus, unlike most projectiles, Pit's aarrows can be used from just about any difference in elevation between you and your opponent. Without platforms he's not so great at racking up damage and generally keeping his enemy under control. I'd never counterpick FD, but it's not really worthy of your stage ban. During stage strikes try to steer away if you can, but it's certainly better to play on FD than, say, PS1.
Battlefield: One of Pit's best starter stages, and potentially a great counterpick against those who are weak from below (ROB included). The platforms help with utilizing your aerials and generally evading your opponent. Plus they play to one of your Arrows' main advantages-- you can steer them to hit anybody almost anywhere, whereas most of the time standing on a different level than your opponent is relatively safe from projectiles. Try to shoot for it during stage strikes if you can, and keep it in mind as a potential, if rare, counterpick.
Yoshi's: You can't go under the stage, which makes gimping you considerably easier. That alone makes this one of Pit's worst stages. Like kupo said, you have to be careful. The platform can help you a lot, but since it's continuous across the stage you often can't shoot down from it, plus it has a nasty habit of being tilted too high or low to be properly utilized. Shyguys can interupt your arrows, and Roger the Support Ghost can save opponents like Ike, Marth, and Mario from being arrow-gimped. Avoid letting it be the starter stage and never counterpick it for any reason, unless you plan on switching characters. If you can, try to collect some information about your opponent. If you thiink they're likely to pick Yoshi's, you may want to consider a ban.
Smashville: My feelings on this are mostly similar to FD, though it's a little bit easier to land bair kills since the KO boundaries are a bit closer, and depending on where the platform is at it can either help you or hinder you. Always try to keep track of where it is in your mind and you'll have a much easier time on this stage. I wouldn't consider it banworthy at all, but I wouldn't waste my counterpick on it. If stage strikes lead to it, that's fine. Pit can compete here as well as almost anybody else.
Norfair: I don't play on this stage a lot. I saw NxC pick it and camp out a Snake something fierce at a tournament once. The multi-level platforms certainly help Pit's arrow-spamming abilities and he has lots of neat tricks he can do with the lava. But the lava from underneath... I think it hurts Pit far more than could possibily help him. It can save opponents from getting gimped, but Pit himself can't generally be saved in the same way because getting hit doesn't give him back his up B. I wouldn't consider it banworthy at all, but as far as counterpicks go I feel there will usually be a better choice, except maybe against Snake or Dedede.