A lot of platform pedals are made of plastics which won't scratch things, like this one. They're pretty much available everywhere for about 10 dollars, though a clear one will pretty much just transfer dirt if it hits. You can also put some duct tape or electrical tape or something over the edges of the pedal (this should essentially be free). Note that certain tapes may leave some residue if they do rub. There are also slightly odd platform pedals which seem to be promising like the Ergon PC2, though I haven't used one .
Another option is folding pedals, such as this one, by Sunlite (these are the cheapest ones available AFAIK, at around 20 dollars). Typically, you push/pull some tabs, pull the pedal out a bit and can fold the pedal up. These are often used for folding bicycles, and should essentially eliminate the problem (provided you buy a quality folding pedal, as if somethings going to go on the pedal, it will be the folding mechanism).
Yet another option is to use a small clipless pedal, such as the Crank Brothers Eggbeaters (the cheapest clipless pedals are around 50 dollars). They're small but you'll need to get special shoes - some SPD shoes (probably another 75 dollars or so) are okay for walking in. Other pedals have a bit of platform, which you may or may not like, such as the Crank Brothers Candy. Of course, if the platform is too big, it doesn't really cure the problem.