When my wife and I travel, we eat a lot of picnic meals...not only because it's easy on the budget, but also because it lets us try a wider variety of local breads, cheeses, fresh produce and cold cuts that we could get in restaurants.
We get flexible chopping mats like this at the local flea market for $1/pkg: http://www.bedbathandbeyond.com/assets/product_images/380/78915310088.jpg
They are inexpensive, very lightweight, easy to clean, and can be thrown out before returning home. These are perfect for cutting bread, vegetables, etc., and provide a nice sanitary surface on top of a park bench or train compartment table.
We cut the 12"x15" mat in half so we have two 12"x7.5" mats that fit perfectly in our daypacks. At the beginning of the trip, we make scratches on the four corners of one side, which reminds us to only cut on that side. In the evening, we wash the mats in the hotel sink with some soap and depending on what we were cutting, maybe some hand sanitizer.