I have a couple of locations that sprung to mind:
Aberdeen Beach itself can be very nice, especially at sunset (if the haar (the fog) is not in!). It's pretty straightforward to find but it might be busy traffic getting there at the end of a work day, worth checking out though:
http://500px.com/photo/7631534
Dunottar Castle and Stonehaven are brilliant places. They are the other side of the city from you, on the South side. Stonehaven has a lovely harbour and Dunottar Castle is a really foreboding place that is great for sunsets.
Stonehaven Harbour:
http://www.pbase.com/mcgarva/image/117153259
Dunottar Castle:
http://www.pbase.com/tinkerb/image/133739844
Balmedie Beach is a well know beach to the North of the City which may be worth checking and there is Nigg Bay to the South of the City again - it leads into a bit of a rough area surrounding the harbour - so maybe not the nicest place to be on a late night.
Marschial College in the centre of town is a very impressive and Granite building:
http://www.pbase.com/mcgarva/image/140705557
If you were to go further West, you'd be in my area - but that's a bit further out than is feasible really! And there are plenty of stunning locations immediately around Aberdeen. There are loads more, but hopefully that provides some food for thought.
This photographer friend of mine and my fathers has some incredible shots in and around Aberdeen, so if you are looking for inspiration that may be a place to start.
http://www.pbase.com/mcgarva/aberdeen
Hope that helps somewhat!