Like Kim recommended in her article, travel during the shoulder seasons. My husband and I generally take our vacations in the spring or fall (though not March/Spring Break time) and usually miss the families, and sometimes get price breaks as well for places that are off-season. This year, we went to Ireland in early May, and took a guided bus tour. There was only one child on the tour and he was about 12 and very quiet, hardly knew he was there. I think a bus tour like the one we had was not "child friendly" at all because most of what we did would be boring for children (viewing scenery, long periods on the bus, shopping, visiting historic landmarks and cultural attractions). So, I would definitely consider another guided tour in the future. The one we did was through Trafalgar Tours, and we were very impressed, it was great.
Also, avoid places that advertise "Children under X age free with two paying adults"...you'll definitely be swamped with the kids at places like that!