To get close to detail out of reach take a zoom lens that has a slightly longer reach. If you're a compact user you'll still be able to capture frame-filling shots if your camera features a longer zoom (20x or above would be good). Having a camera with a vari-angle LCD screen can make it easier to frame your shot when working with a tripod at its maximum height or when you're working hand-held with your arms up above you but it's not an essential feature.
Most pictures you see of churches, cathedrals and other tall structures show the whole, impressive structure but by cropping in tightly you can highlight the fantastic repetitive detail, make an interesting pattern and shoot detail you don't always notice in the wider shots.
If you can get on the roof or balcony, as well as gaining you a great viewpoint of the city you can often find interesting statues/gargoyles projecting out from the walls. As they don't move they're an easy target and most are so beautifully sculptured that several varied photographs can be taken. However, as not all buildings give you access to their roof, you'll probably end up shooting from the ground where you'll need to use the longer reach of your telephoto or zoom lens to bring the detail to you.
The problem you have with using lenses with a longer reach is that they magnify objects, which is of course what you want, but this does mean that even the tiniest of movements can create a large amount of blur in your photograph so make sure you have a tripod and stick to quicker shutter speeds when possible. Using a lens which features Vibration Reduction (VR) will further minimise shake. If you're shooting detail such as weather vanes where the sky will be your background fit a polarizer to darken a blue sky and give more contrast to the shot.
Once you begin to search you'll be surprised at the amount of detail you'll be able to fill your frame with. Of course there's gargoyles, clocks, windows, spires, sundials and weather vanes, but a little closer to the ground you'll find stone carvings present and sometimes intricate detailed wood carvings on the exterior walls around doorways and above windows.
Filling the frame with repeating patterns such as brickwork or tiles on a roof can create interesting abstract shots. Just fill your frame, watch your shutter speeds if you're working hand-held and make sure you're focusing accurately as blur really doesn't work in this type of shot.
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