There are two main areas. One is the headland, which extends from the east end of Torry to the lighthouse, and then St Fittick's Park, which is inland from Nigg Bay on the south side of Torry.
For seabirds, go to the east end of the headland. Seawatching is best from around the foghorn. A scope is helpful, but you should see auks, Kittiwakes, Gannets etc. with binoculars. Migrants can potentially be anywhere. Torry Battery is good, as are the allotments and the north bank. Open areas can pick up things like Wheatears. St Fittick's is also good for migrants but there is so much cover they can be hard to find there. That's also the place for Snipe and Jack Snipe, although there haven't been many lately. Some may appear in the next few weeks but they can be tricky to spot. Water Rails are there and are often easy to hear. This winter, they've been a bit difficult to see because of high water levels. Winter is always best for seeing them.