i havent been to san ignacio in 3 years, but certainly in the town proper there are little restaurants, and i remember some little places on the road. these places are quite small, local or family owned and would NEVER make it to the internet. i remember SI had a really good chinese place, and i think there was a so-so restaurant in the SI hotel. i remember an ice cream stand in the town square.
if you pass any jungle lodges like chaa creek or duplooys, they can feed you too. make sure you try some yummy & refreshing limeade.