When we travel, since most hotel rooms have a small refrigerator, we always get some basic breakfast items that the kids can eat in the morning, such as fruit, cereal, milk, instant oatmeal, yogurt, etc. If they don't provide any dishes or utensils at the Anchorange, just pick up some paper plates, bowls & plastic utensils at the market. I find it much more relaxing (and a big money-saver) to have a simple breakfast in, rather than having to get everybody up and out early in the morning. (Plus the wait at many of the popular breakfast places in the summer can be quite long). There are two major supermarkets in the Ogunquit area, one south of Ogunquit in York and the other north of Ogunquit, in Wells. I think they're both Hannafords.
On the days you do decide to go out for breakfast, there's Cafe Amore (good, but small and fills up quickly!) in Perkins Cove, or you can pick up muffins & coffee at Bread & Roses bakery on Main St. I believe there are a few other coffee places w/baked goods here & there in town. Otherwise, as I recall most of the other places that serve a full breakfast in town are along Route 1 going north toward Wells -- we especially love Bintliff's for breakfast -- it's not inexpensive but worth it!
Have a great time!