The Lonely Planet Thorn Tree forums are a great source of info and I think there's some kid branches in there.

For backpacker style accommodation, and just general crowd avoidance, I recommend going in May or October. In these months, very few universities around the world have holidays so backpackr numbers are lower (also means that more interesting people - long term travellers - are around)

It depends what you want to see while you're over there, what you're into. Food, that's a great start. What about natural features, historical features, cultural features, relaxation?

I loved Germany for budget travel - travel and supermarkets are cheap, most hostels have kitchens, many have family rooms too. Northern UK and Scotland hostels struck me as being very family friendly too, particularly the HI hostel in Newcastle.
Rail passes don't always represent a great deal, depending on whether one or both of you has EU citizenship (InterRail is a good deal in Western Europe, waste of money in the East, I wouldn't bother with Eurail)

Festivals: Hmmm, I went to heaps. Most not child friendly Anyting big makes accommodation harder to get and sometimes more expensive, like trying to get a bed in Edinburgh for Edinburgh Festival, or Munich for Oktoberfest etc.

I'll be back with more if you like...