It could well be warm enough to swim. We do have some hot days (as Lucy said) and our ocean temps are warmer than those down south.
If you want to stay near the beach I recommend Bondi or surrounding suburbs in the eastern part of the city (Bondi is very popular with tourists).
Paddington is one of our ritziest suburbs and is well placed between the city and eastern suburbs beaches. Lots of great cafes, restaurants and shops and very pretty architecture. Lots of Australian designers have retail stores there. Can be expensive but there is no charge for looking
Closer to the city there is Pyrmont/Darling Harbour, which is easy walking distance to the CBD. Darling Harbour has lots of restaurants and tourist attractions and good access to the harbour for ferry rides etc. Pyrmont has a more city (high rise) feel than Paddington (which is a more leafy suburban area, full of lovely terraces).
Feel free to PM me when you have some suburb candidates in mind, and I will try to help out.