Take your time, keep your camera handy, and be alert for good photo opportunities. Unusual lighting or perspective often transform what would have been a mundane image into awe-inspiring one. Portray your subject from some angle other than eye-level. Frame vertical subjects vertically. The light of early morning, sunset, fog, etc., is often dramatic.
Overcast days are good for people pictures - just leave the gray sky out of the photo.
If you need to capture sound and action, consider taking along a compact camcorder rather than a camera. Don't get so wrapped up in trying to record the trip that you don't have time to enjoy it. When you get back home, edit your pictures ruthlessly. Show only your best. Fight the urge to produce a documentary.