When you say you can't shoot at the same angle, do you mean because it's difficult to figure out exactly where the photo was taken originally, or do you mean it's impossible because of some physical change, i.e. new construction, demolished building etc?
If it's the former, just have a copy of the original photograph with you, and try different locations and angles, paying attention to specific features in the scene. Try to match areas at the corners if possible. If the corners are all correct, then the rest of the photo will be also. A complicating factor would be if you don't know what type of lens was used originally. If you can't be sure the focal length matches, it will be extremely difficult to get the picture to look correct.
If you don't physically have access to shoot from the same location, then you'll need to get as close as you can, and then correct the perspective in Photoshop.