Wide Angles lenses are great for this, in the city you really would only need a telephoto when trying to focus in on a specific object maybe a gargoil or whatever those things are on the older building or maybe an animal in a park.
Make sure you go out at different times of the day, the different types of light will give you many different types of photos even taking the exact same photo. What works during the morning may not work in the afternoon.
Also try different ISO settings. I have some photos of fountains/water features taken in Sydney just as was really getting dark, used the ambient light and ISO1600 and the photos are really nice (to me).
Also look for reflections on skyscrapers, especially when reflecting the building opposite.
Try getting evening lights in a busy area, maybe a longer exposure from an elevated walkway, focus on an object and see if you can blur the rest of the frame so it shows motion and not just still life. Or go the opposite, blur one object and still life everything else.
Hold the camera up in the air and shoot over the crowds walking the pavement. Shoot things written on the ground like directions for pedestrians.
Pretty much anything and everything is fair game. make sure you have enough memory and just click away, try and avoid reviewing too much on the run unless you want to verify a specific pic worked.
