Fox-
Preferred Neutral Stage: Lylat Cruise
Lylat Cruise has the natural stage "tilt" that can potential screw over Fox's Illusion recovery, although the ceiling may be an issue. Both sides have to be careful with their zoning, although ROB can really rack up some damage here. For some reason the platforms of Lylat don't feel as dangerous as the platforms of Battlefield, although that may just be me.
Neutral Stage to Avoid:
Battlefield or Smashville. Battlefield because the platforms, while helping ROB a bit, will making Fox very difficult to fight against. Smashville because of the low ceiling allowing Fox to score an easy U-Smash kill after a bit of juggling, or even U-Air kill. Considering a key trait of ROB is his survivability, you don't want to lose that.
Counterpick Options: Frigate Orpheon
Standard ROB counterpick. No ledge on the right side 1st transformation, yaddayaddayadda.
Ban Options: Brinstar
This stage is a huge pain in the butt. The ceiling isn't friendly, the sides are close, the platforms and irregular surface make ROB work extra hard, and the acid can negate a lot of ROBs kills (although dealing some percents to the opponent is nice).