When photographing interesting cities, you'll find it very convenient to travel light—a point-and-shoot camera will free you to concentrate on compositions and allow you to respond more quickly to great photo opportunities. If your camera has a built-in zoom lens, use it at its widest setting for broad views, and at its longest setting to close in on architectural details.
The urban whirl offers a multitude of opportunities for great shots—architecture, open-air markets, landmarks, and more. The kind of photos you'll find will depend a lot on the personality of the city, and in many cases, great features of any given city are only blocks apart. If you're in town for just a short time, you may want to take a short bus tour to orient yourself and find good picture ideas.
From a high location, patterns appear in the grids of streets and rows of buildings that aren't apparent at street level. Distant views can give you a beautiful skyline. If you're unfamiliar with the city, the most challenging part of photographing cityscapes is in finding a great vantage point. But going out of your way to locate great places from which to shoot is very worthwhile.
Many major cities have observation decks that offer great overviews. When traveling, request a hotel room on an upper floor. This way, you can shoot from a balcony or window (make sure to turn off room lights to avoid reflections when shooting through glass). Some hotels and other buildings have rooftop bars and restaurants, which are easily accessible. This is true of some hotels in Las Vegas, which afford great views of the strip nearby. Nearby hills or bridges also offer good spots for expansive views of the city, such as views of San Francisco photographed from across the bay. Other sources of good photo spots include postcards and travel brochures of the city you're planning to visit, and many taxi drivers can tell you about great locations to photograph their city.
Taking pictures of cityscapes at midday will yield very dull results. One of the most exciting times to photograph a city view is at dusk—cities and buildings take on a completely different look and feel during this time. Use a fast film (ISO 400-1000) if you're hand-holding your compact camera. Find a location from which to shoot in the afternoon, and go back just before sunset. A few minutes before the sun goes down, try to shoot pictures from the west to catch the last rays of sunlight illuminating buildings.
After taking some sunset shots, watch how the light changes as the sky grows darker and the lights in the buildings become more visible. With some lingering blue light in the sky, you'll get some great shots of glittering city lights against a still-colorful sky. Finish shooting skylines when the sky is totally dark, as the building lights will simply record as disembodied lights in the sky. When it's completely dark, concentrate on filling the frame with well-lit subjects and avoid large areas of unlit space.
For some especially colorful photos, try shooting city streets at dusk after a light rain. You'll find that street lights, neon signs, store windows and car lights reflected in wet streets make striking photos. Take lots of pictures—or use a high-capacity memory card when shooting digitally—to ensure getting some great pictures after dusk.