Lighting is the biggest barricade between a mediocre picture and an "oh my god I wish I were there" shot. Try to shoot your photos during golden hour: the time shortly after sunrise or before sunset. The sun is softer and redder and provides beautiful lighting for photos.
For any other time of day, think about where the sun is before you take a picture. If you shoot straight into the sun, the photo will come out under- or overexposed. If you shoot with the sun coming across your face, you will be left with weird shadows. As a guideline, you always want the sun perfectly at your back.
The worst time to shoot is around high noon hours, especially with full sunlight and little to no cloud coverage. If you are trying to get a good shot around this time, place yourself in the shade (under a tree or leaning on a building) to minimize shadows on your face.
Pro Tip: I like to photograph during sunrise hours the most, not only for lighting but also because of how clean and deserted the shot will feel. While waking up early might not sound fun, I promise walking the streets of a tourist-heavy town with no one around is a fantastic experience.