My class makes post cards for our post card exchanges. We live in Northern NJ- not touristy so postcards would not represent our area of the state and parents arent going to really find them anyway in the local stores. The post office has blank white post cards- we use the computer to search for our state symbols to put on the cards.
I would ask the parents first. Sometimes have postcards lying around the house. I think even if your town doesn't have postcards, you could do the next largest city. Also, check with your chamber of commerce, tourist office (even the smallest towns have something) and you could take a photo of your school and make post cards with it.
The year before last I was able to get all of the postcards we needed donated by visitors bureaus in the area. I have just e-mailed 3 to see if I can get an adequate number for this year's postcard echange.