I will second traveling light- even in NYC in winter, it’s one carry-on bag each for us (it doesn’t mean you look like shit- we stay at the Ritz and go out to very nice places- it just means “pack smart”). Tying yourself to too many big bags is ridiculous, marks you as a stupid tourist, and slows you down and distracts you. If at all possible, use a backpack instead of a rolling case- having your hands free comes in very handy.
Many places have stuck with me in odd ways. If you put me on a plane and blindfold me as we’re landing, I will know we’re in London as soon as the door opens, because of the smell. I have no idea why, there is nothing particular I can identify IN the smell- it’s just… London.
Talk to people. Strike up a conversation with your cab driver, your waiter- find out if he’s local or a transplant, ask him about local food/sports/whatever. You will rarely be disappointed.
Walk as much as you can. The closer you are to the ground, the more you will see, learn, experience and enjoy.
Don’t stick to tourist areas- get out! If you are looking for a place to eat, pick a place that doesn’t have anyone in it who looks like you.
Ask the waiter about the house specialty, then order it.
Take 1st world medicines with you. My doc will give me a 'script for Cipro before I leave, with instructions to take it at the first cramp if I’ve eaten something dodgy, but I have never needed it, not even in the jungle in the Yucutan eating at a local Mayan place.
Take your children with you. Travel gives you a new perspective on your own life, and that is at least as valuable to young people as formal education, maybe more so. Find a project for them before you go- a report on what you’ll be seeing (then they have to be the tour guide!), or find a local charity where you’re going and have the kids get donations together to take with them.
DON’T LOOK/DRESS/ACT LIKE A TOURIST. Leave your nice jewelry at home. Dress like most other people you’ll see walking around. Or, if you’re American, dress like a European tourist- you’ll still be better off. Relax and “go with the flow” as much as you can- you’ll be happier and so will the people around you.