Shiek and Fox seem to be the biggest counters to Peach now. Marth and Captain I think are much more even matches that really depend on the stage. However I still believe that Peach has some monster counterpicks agains Shiek, such as Mute City.
I'd like to see how people have done at DK64, I know Peach owns at Mute City and most people go to Dreamland, but I've found, Dreamland to be a rather even matchup, simply because the platforms and stage is massive and it can be a challenge to knock Shiek off the stage far enough to edgeguard her.
The ceiling is pretty high, but I think Peach can knock shiek off the stage better, but she can also avoid Shiek's platform camping. It also seems like it is easier for Peach to recover at DK64 than it is at Dreamland. Also Peach can sometimes float over to the barrel if she is needle spiked.