I think Steve pretty much covered it. You'll spend as much money as you spend (not very helpful, I know.) Certain countries such as GB and 'Swiss' are more expensive than Spain or Germany, so expect to spend more there. London has the advantage of a lot more free museums. In Rome, most of the churches are free while the museums aren't. In Florence, almost everywhere charges at least a small admittance fee. So it varies depending on what you want to see/do.
Cities are more expensive than the countryside, so if your family is driving you around and you stay off the beaten path, you could probably do it on $100/day for two. If you're in a city such as Rome or Paris that you don't want to drive around in, you'll have to figure parking costs plus any public transportation you use while in the city.
Lunch is cheaper than dinner, so it works well to have a bigger lunch and not buy dinner or buy something at a store and have a picnic. Of course, traveling with family, you might have less say in the matter.
General rule of thumb: pack half of what you think you need and twice as much cash. :-)