Maybe some fruit or something? Hmm...
Maybe something that relaxes the characters is good for their stamina?
I was thinking food could play some sort of 'Fantasy potion' role.
Eating shouldn't immediately restore stamina, but eating enough food puts your character into a 'well fed' state, and then when he or she is idle, or resting... they gain stamina much faster. This would encourage eating, but not make it a over-necessary part of the game. I can't imagine everyone wanting to have to go and eat every hour or so.
You could also have sour food like lemons that really perks up a character, and spicy food that gives you an extra energy kick. The downside is that you could only eat so much before becoming full, or some types of food could upset your stomach, making it so you can't eat special foods for a while.
Water could also play a part, helping upset stomachs perhaps?