In general, sheik likes platform stages. Also in general, falco doesn't like platform stages. Therefore, in general, pick platform stages!
Battlefield and WW are probably some of my favourite levels as sheik (especially WW, which is probably sheik's best stage) and their platforms can help you get around his laser game, although they also help his combo game, so it's not foolproof. The platforms on these stages just help her so much for stringing together combos. FD is probably the worst stage for this matchup and should be your ban against a falco player just about every time. Smashville is overall pretty meh. The platform doesn't really do much when its over the stage, for either player, since it spends the majority of its time on the sides. Occasionally it'll create platform traps, but the sides are where you really need to be aware of its positioning. It can provide both a safe-haven on a return for a character or set that character up to easily be edgeguarded during their lag, depending on how well the edgeguarder covers their options. Since the platform on SV rarely actually acts like a standard platform, I'd argue that this stage favours falco more than sheik and should probably be avoided in a counterpicking situation. YI is nice if only because it screws up his laser game more than any other stage, with the stage itself absorbing shots for you when it's positioned right. The height and angle of YI's platform can be... inconvenient at times, but sheik is typically pretty good at ****** opponents stuck on a platform above her, and I believe you can do some aerial tricks by jumping from higher ground to lower ground on this stage. Lylatt is the ultimate mixed bag stage. The three platforms don't offer any particular advantage to a 2 platform setup with a 3rd higher platform, and tends to force play to be more grounded than other platform stages. Sheik's comboing is most certainly helped here, but I don't think it's helped as much as on BF or WW, where she can be all over the stage comboing you. When the stage is tilted down and falco is uphill from you, falco pretty much hates you, since pretty much everything he has is less effective. When the stage is tilted up and falco is downhill from you, you can pull off some aerial tricks on your approach, but his laser camping and general approach options become so much more effective, you'll want to take to the platforms, which while sheik may love platforms, she typically likes it when the opponent is the one on them. The tilting can also drastically screw up falco's recovery (and yours, too, if you get careless), so all in all, it's probably a fairly solid cpick against him, but not my first choice.
edit: I forgot PS2. The platforms on PS2 aren't nearly as handy as on stages where the platforms cover the whole stage, causing the stage to play more like a flat stage than a platform stage, although the platform traps here can still be nice. Falco probably likes this stage better than you.