The rule of thirds

Divide your frame into thirds horizontally and vertically, like a tic-tac-toe board. Some cameras will even draw these lines for you on the screen (but won't include them in the final shot). Ideally, keep your main subjects where those lines intersect, as eyes tend to gravitate there first. If you're shooting a horizon or skyline, have it match one of the imaginary horizontal lines. For shots of people, have the eyes fall along one of those lines.

Lighting matters

You'll typically get the best lighting shortly after sunrise or before sunset. During these "golden hours", sunlight is softer, and subjects look better.

But it's not practical to constrain your sightseeing to just a few hours a day. At least try to avoid having the sun shine toward the camera, as that leads to dark subjects. If you can't avoid it, some cameras have an "HDR" mode to help.

The camera basically stitches together separate shots of the subject and the background adjusted to different lighting conditions. Turning on the flash yes, in daytime can also help light up an otherwise dark subject.

At night, though, you should try to keep the flash off, as light distribution can be intense and uneven. Cameras have become much better at low-light shots, such that you're often better off working with ambient light. Bonus tip: Use the flashlight on a friend's phone to add a bit more light to a scene.

Know the limitations

While many cameras now have auto-focus, they don't always pick out the subject correctly. If you're shooting with a smartphone, just tap on the intended subject on the screen. This also has the effect of adjusting the exposure to that subject, rather than something in the background you might not care as much about.

With most smartphones, you're just getting a fake zoom, also called digital zoom. The image isn't actually getting larger it's just stretched out like elastic using software. It might be fine on the screen, but it'll look fuzzy blown up on a desktop web browser or printed out for a photo frame.