Traveling using a family is a completely different beast than traveling as a couple or alone — I’ve done both times that are numerous, as well as the two experiences do not even look connected.
Pack light. That means you’re pulling everything you package about for miles if you are traveling in multiple cities.
Walk everywhere (with some mass transit). The best means to explore a location is by tour bus, not car or foot. You cover less ground on foot, when you walk it, but you only really visit a location. Bikes would be next best, although not manageable for a sizable family.
Get lost. Until you get lost in it you do not really learn a place. You also discover the most surprising things when you allow yourself to get lost. Roam, investigate, find, be surprised.
Use your trip as a language course. Knowing we were going to Spain, France and Italy, we learned a bit of the languages before we left. The kids had fun learning where is the bathroom, and to say hello, thank you, among other phrases. I think we all studied a bit about languages and cultures, and it turned out to be a fantastic start, although we never got fluent. There is not any better approach than seeing the nation to practice a language.
Avoid tourist traps. If you go to highly touristed places, avoid restaurants and the shops that surround them. They may be aimed in the preferences of tourists instead of locals, and costly, awful quality.
Have something to keep children busy on trains. The kids get bored, although I do not mind train rides at all. So they each have some type of apparatus, such as a game device or an iPod touch, to play games, listen to music watching films. Not my favorite thing on the planet to allow them to do, but so far much better than complaints of being bored for a number of hours.
Rests are great. We often leave each morning for researching, then come back after a late lunch for a rest. The children get tired so do we, and walking around in sunlight. A rest of an hour (or three if you’re jetlagged) is a great thing, and we typically would head out when the day was cooling down for some evening sightseeing and dinner…