One of the easiest ways to change the look/feel of a shot is to change your point of view so you're shooting from high up and even though climbing a mountain may be the first thought that springs to mind, you don't actually have to climb that high to give your images a different twist.
For those of you using DSLRs with interchangeable lenses, pack a wide and telephoto lens in your kit bag as you'll be able to capture both sweeping vistas and focus on distant objects / scenes. This doesn't mean you can't use a compact or a more pocketable sized mirrorless model, in fact you may find these types of cameras are better for long walks up hills as they're lighter meaning you'll be carrying less weight. A tripod's always handy and if you are planning on going for a long walk, wear suitable clothing, pack food and drink and always tell someone where you are going.
So, why go to the effort of climbing up stairs or heading up a hillside? Well, shooting down on to a popular subject will instantly give you a different take on an overly photographed scene. You may also spot something else to photograph while you're up there as well as use the streets and roads that are surrounding your subject to add an extra dimension of interest to your shot. Shadows will add texture to your shots while looking for a building that can act as a main point of focus in your shot will help give it dimension, making it easy for the viewer to distinguish between foreground and background detail. If you have a longer lens, try zooming in to one particular building, picking out detail you may not necessarily see from the ground.
Shooting through glass isn't ideal so instead of shooting from tall, modern buildings in towns and cities where there's windows in your way, look for places that have balconies and observation decks to shoot from. If you're in a city that has a giant wheel in the middle of it, take a ride as they move slow enough for you to capture quite a few bird's eye views of the city. Bridges and steps will also be able to give you the added elevation you need to capture a few shots from higher up. Further out of a town, try climbing a nearby hill so you can shoot down on the buildings and lights at night.
If you don't really like heights you don't have to climb a building to give you a different point of view. Simply standing on a ladder, extending the height of your tripod or even using a kite or pole to fasten your camera to will give you a few more meters of height. If your camera has a tilt screen, like the Samsung NX1 does, you'll be able to hold the camera up at arm's height or work with it when your tripod's at full height without struggling to see what's on screen. As a result you'll be able to shoot from a variety of angles, making for a more exciting collection of images.