I have eaten out quite a lot over last few weeks (school holidays, Easter and birthdays).
I do try to plan ahead in that I look at menus online so I know in advance which restaurants are better than others, I also have to take into account whats on the kids menus and that fact that I am also a veggie.
Many places have salads or as others have said I ask for swaps or just don't eat the bread/carb stuff (kids eat the buns etc).
We have a number of 'regular' places that we know we can all have something nice to eat such as Prezzo (i have salad), Harvester (staff have really good knowledge for swapping carb options - lots of choice for low carb and cheap food), nandos, giraffe etc (I rarely eat out in non-family friendly places!)
In terms of local/independent cafes, again I know of a few near us and in the two cities we visit regularly but occasionally we visit other areas and it can be very difficult (if I ate meat I would order meat/fish salad or a quiche and scoop it out of pastry shell) last week ONLY veggie option was a soup served with two enormous pieces of bread (kids ate the bread after eating their own lunch

).
Sometimes I order a few starters/side dishes to make up a meal, most cafes are happy you are spending money so don't really care if you order strange combinations. I try my best but sometimes its not perfect.
We often have picnics (usually in the car as its too cold in UK in summer

) I will have a salad or buy cheese, olives and quiche (scoop filling out of pastry).
On days out I will take snacks for me and the kids (nuts, olives, cheese for me) to tide us over if we can't find a cafe that serves what we want.