Redhook's pub, Forecasters, has a casual attitude and admit minors, so it makes a great family destination.
It goes without saying that they have great beer, the food is not bad either, but the best bit is in the summer: the beer garden out back. It's great for kids as it is pretty well walled in, and nothing beats having a beer, in the sun, with your family. Its also a good place to arrange meeting your not-with-child friends, they can stay later of course when you bail because its late/little-one-is-tired/you-are-tired. Your friends could partake of the outdoor cinema after you leave, for example, in the summer months.
They often have live music in the evenings, and minors need to exit before then: a wise rule for many reasons.
Disadvantages? Well there are no baby changing facilities, though there should be soon (I emailed them and they are looking into it). There is also no actual kids stuff to play with, so remember to take along enough toys etc to keep them entertained, especially if inside (they can always run about if you are outside).