I'm thinking Jungle Japes and Luigi's covers him pretty well. FD even if we wanted to camp him to death.
The first two are probably Falcon's best stages, or at least close. I know Peach is pretty light, but it takes insane amounts of damage to KO Falcon at the top blastline because of his weight and fall speed there. And he has knee shenanigans at Luigi's Mansion. Basically, on Japes, Falcon just has to DI everything up, and can abuse Raptor Boost for a relatively safe spike attempt, and the platform allows for decent amount of uair spamming. If they are your most comfortable stages, it's not like Falcon will **** you there or anything, but they probably help him more than they hurt Peach. FD is decent against him, it's probably the best neutral for camping like you said, but Falcon is the one of the best against camping out of all the characters with no projectiles. He has extremely high jumps, bair or jab (among other things) can stop turnips, and Falcon has an extremely fast dash, so I don't think camping will be very effective, but FD isn't a great stage for Falcon. Norfair is the only other stage besides Japes and Mansion that you wouldn't want to take Falcon, imo.
As far as bad stages go, I actually took a lot of time thinking about it and asking someone, and I really can't think of any terrible stages, although there are some counterpick stages I don't play much. The only thing, to me, that would be a pretty good cp for Peach against Falcon is Frigate Orpheon. I don't think it's a terrible Falcon stage, but he has a crazy edge sweetspot reach on Falcon Dive, and without a grabbable ledge on the right side of the first transformation, recovering is tougher. And, if the stage flips when both are in midair, Peach has a far better horizontal recovery, but watch out for Falcon Dive latching onto you, Falcon can use it again afterwards.
