Best way to remove scuffing on interior plastic?

No matter how careful I try to be, I always seem to hit my feet on the cup holder on the door card, and the front of the seat trim when entering/exiting the vehicle. Before I start experimenting, what do you guys use to remove shoe scuffs from the plastic interior trim?

I use either brake clean spray or carburetor spray cleaner. I wipe the door panel first with a damp rag and then a terrycloth towel with some of the spray solvents on it. Then i wipe it with a another cloth that has some ArmorAll sprayed on it. That method seems to do the trick!
The way that cup holder sticks out, it's just begging to be kicked.