These are my thought and reasons. I take it that the purpose of this site is to display recipes. You want those recipes to be classified as breakfast, lunch, and dinner. OK.
Don't use arrows to obtain the recipes, use a multi-tiered menu. Why? The menu will show the recipe names at a glance and you can navigate right to it, using arrows makes getting to the needed recipe hard. Let's say you want LUNCH->RUBIN SANDWICH, but you have 15 soup recipes before you even start displaying sandwiches. I'd go elsewhere, wouldn't you?
I'd next use a three tiered menu to further classify the recipes. LUNCH would show SOUPS SANDWICHES SALADS SIDES
You can find code for this by goggling "simple three tier menu".
I'd do a header, next the horizontal drop-down menu, and that leaves a lot of space for the recipes. You don't need a footer so you have a simple html design.
I'm worried I have too many divs.
Don't think there is a limit on the amount of divs you can have, maybe the browsers have one?? But if that becomes a problem we can change strategies. Also, if a lot of divs give us long load times, we might want to look into iframes or ajax, but hold off on that.
Hope this points you in a direction.