I'd love to do the budget backpacking thing, I'm dying to see Europe. Hopefully when the kids are a couple of years older we can leave them w their grandma and take off to see the world for a few weeks.
You'll probably have to do it with the kids - a few weeks isn't enough to immerse yourself in culture. You'll just end up swimming around in the western bubble. Live an alternative life style with your kids, show them the world isn't a scary place. Hell, move to Europe! Just some ideas.
Or the Vogel family - http://familyonbikes.org/blog/?page_id=10 ("The Vogel family left June 8, 2008 for a 2 1/2 year bicycle trip traversing the Pan-American Highway from Alaska to Argentina.")
