There seems to be a lot of hullaballoo about taking children to restaurants lately. Nice restaurants, family restaurants (I don't know about the difference, I think a family restaruant can be very nice...), fast food, and even child-based restaurants. I think that a child should be able to behave in ANY of those, and if you want to treat your children to a nice meal out then go ahead. There is a great feeling in being told by a server how well your child behaves, I promise it's worth the work!!
There's a few ways to make it a little easier, and even though some are obvious it can help to hear then from someone else as well.
First, explain to your child that they are to behave like the adults around them. If everyone is sitting quietly then they should a well, but if it's a children's restaruant there's more room to wiggle on that, they can play the games and use the toys, and even speak at a different volume sometimes.
Practice manners and proper mealtime behaviours at home.
Pack something for them to do. Either your phone, a book to look at the pictures, something to colour, a puzzle, or even a quiet toy/doll. I don't recommend cars or other vehicles, anything with small pieces, or a special gift from grandma. Sometimes things happen, so take something that can be lost without the world needing to end.
Pay for your meal after you order. You can request to pay when you order, then if you have something else you just pay the remainder later. Most servers will be happy to do this if you explain that you just want to make sure it's paid for in the event a child acts up and you need to leave quickly. If your child starts screaming or won't listen then you should remove them, if you both know it's paid then it's more incentive for them to behave, as they know you can just get up and walk out. (I've only had ot do it once)
Remove them if necessary. I know it's hard, and no one wants to do it, but it works very quickly and rarely needs to be repeated. Once they know you will follow through their behaviour will likely be done next time.
Make a game of good behaviour. Examples could be making it a tea party for the princess, pretending your hiding and want to eat your meal without being found, whoever uses the best manners picks dessert, or even the best behaviour lets them pick the place next time. In turn, if you run around and have fun when they choose a picnic or Chuckie Cheese, then you get to pick your favortie after that.
Take them to the same place more then once. The first time you go anywhere it's new and curiousity peaks, they will want to walk around everywhere and see everything, the second and third time they are comfortable enough to sit and not worry about what's on the wall behind them because they already know, but not quite comfortable enough they act like they own it.
Enjoy your next meal out! :)