We do weekend morning eating out - which generally spells brunch for us, lunch for DD. As someone else has pointed out, brunch menus with eggs, toast, sausage, fruit and fruit juices are generally OK with all ages.
DD is now 2.5, and we entertain her by looking / walking around whilst food arrives, probably going to the toilet, playing at 'paying' and lining up money / plastic cards, letting her be a big girl and spreading butter on her own toast, cutting our food, maybe some crayoning etc etc. Being outside also helps for some reason.
Most success with local informal cafes (we're over-served in east London for breakfast options), followed by chains like Giraffe and Pizza Express - their dough balls!
We've also done smarter breakfasts, eg the Delauney and Riding House Cafe - both worked well, but it was definitely a case of order, eat, leave and not much on the lingering front. Still, we, as parents got the eating out hit, and when you leave, it's still only 10am and no baby-sitting costs. Magic!