At the same time, don't hesitate or edit your options before you even take the picture. If you see an image you like, trust your gut and shoot first, reconsider later. You can always buy more film. Over time you'll combine these practices and your picture taking will become more instinctual.
It's not just your subject, but rather the relationship between all the different elements, shapes, and colors in the frame that dictate the tone and mood of a picture. Placing your subject directly in the center of the frame is the single most common mistake made in amateur travel photography. Mentally divide your frame into quadrangles, or even smaller segments, and pay attention to the borders of these areas. Try putting your subject, whether it's Aunt Vera or the Eiffel Tower, in a corner, using the remainder of the space to show the surrounding context and tell a story.
When photographing people, don't crop rudely. Putting their face in the middle of the frame means you might leave a disproportionate amount of blue sky above them, and cut the bottom of the picture off at their chest. Crop at your subject's waist, or step back to include their feet. If you're up close, crop them just below the shoulders.
Pay attention to scale, too. Your final picture will look just like it does through your camera, so don't be lazy. Walk closer to cut out the excess scene you don't want to include, or use a zoom lens to home in on your subject. Also, explore different perspectives. Try kneeling, or even shooting from ground level. Sometimes standing on a chair, or some other el-evated stance can help you include some essential elements that help make the scene all that more magical.