Ubud may, on first impression, seem like a heavily built up tourist town, but it's surprising how quickly and easily you can find yourself in a purely pastoral setting surrounded by rice paddies. You don't even have to find transportation to do it, as there are several places around town where a simple turn off a busy street will take you into a different world.
If you're in the mood, there are some paths that will take you on a walk of two or three kilometers through the countryside. To get a taste of this, you can just visit the highly recommended Sari Organik restaurant, which involves a good walk through the fields. The directions are contained in my review. The path to Sari Organik continues further through the fields and eventually meets up with Suweta Street, which runs up the hill from the Art Market and Palace area.