Great question that every bike tourer must answer.
When I leave the stove at home, invariably I wish I had it. When I carry the stove with me, I use it all the time.
Light weight stove that uses coleman fuel does the trick as long as there are at least two in your party. One to carry the cooking gear, the other to carry the food. One to cook, the other to clean.
On my recent tour last summer, I found that I cooked oatmeal in the a.m., tea at lunch, and then noodles, at dinner.
Eating in cafes became uninsping and the camp ground was our preferred dining spot. That being said, occasionally when you came across a great diner, with terrific food, we just strapped it on and ate our faces off.
I am planning on biking the Natchez Trace with my 10 year old son this summer and I can't wait.