There isn't much more Peach can do in PM that she couldn't in Melee when in neutral, but I'll try to think of small examples you might be able to integrate.
Utilt can now shark half a platform (Battlefield size obviously, not Norfair size or something huge like that), much better than her lackluster headbutt in Melee.
Her side special can cover pretty much all tech options on a platform except a getup attack (because it still has terrible priority, you really don't want your opponent to have any hitbox out, not even a jab). It's also now useful for finishing combos, especially with Fox's typically high hitstun. Some Peaches also use it for tech-chasing because she's incredibly slow and this move gives a pretty big lunge forward, but I have reasons to believe that dash attack is better. Still, try it out.
When caught in Fox's shield pressure with a turnip you can roll away from Fox and throw the turnip towards him with a glide toss, and you might get a conversion or you might risk the reflector doing its actual job. In Melee, you could only throw the turnip in the direction you were rolling, and your glide toss only went half as far, so this is an improvement. Aerial glide tossing is relatively worthless in this MU other than to suddenly change your horizontal momentum midair, and even then this scenario is even rarer than using a turnip to get out of shield pressure.
I can't really think of much else you can do. I would recommend watching some high level Peach vs Fox videos in PM but all the high level Peaches come from Melee and don't even integrate the PM stuff, so you might as well just watch it in Melee.
The last thing you could do is wait for the next patch (*knock on wood*).
