Many characters can abuse platforms against them, including spacies, Falcon, and swordsmen. For this reason I tend to stay away from BF, WW (although WW is pretty good against characters that can't abuse platforms as well). Even though I tend not to like it in general, Yoshi's Island is pretty good for them since the platform is so wide it still allows them to use their horizontal mobility on it while avoiding quite as much platform abuse (examples: marth can't cover your options from below you as well since you have the whole wide platform to work with. Fox can't camp the platform as well because if he wants to drop and shine you, he has to drop through it as long as you stay bottom center.)
Other things to keep in mind include: blast zones. As 941 said, narrow side zones allow your opponent to kill Nana easier. High ceilings help your survivability because they're floaty. Stage size. Although they have good horizontal mobility, you may want to go with small stages on which you can bully people with your double attacks and set up for handoffs the quickest.
But it all depends on your opponent's character, honestly.