Maroubra beach fishes well for the usual species - salmon, tailor, bream, whiting, blackfish
Find a good gutter and throw ganged hooks with a pilly on it
If you get it right the nth end fishes well for blackfish - it's no big secret - just head down there look for the where the weed is growing, pick some off the rocks and have a go.
As alasdair has mentioned the sth end is great, but it is a rock platform and you need cleats and you need to be careful - fish this in a southerly swell only. So you don't walk all the way out there, park at the nth end on the hill and look across.
Another good spot out there is The Blessings - you are high up and it is a safe spot. It can get busy, but if you get there early enough, you can pick your spot. You catch pigs, bream, blackfish etc here. Do a search on this website and you will find out more.
yarra bay is good for flatties and it's totally safe
Bare Island produces squid at night as does Malabar
I have caught blackfish off the beach at nth coogee, but it can be a challenge to fish it in summer. Go early or late to avoid the crowds.
You can actually fish Clovelly pool (just not for groper). Give it a go at night when all the crowds have disappeared.
On a CALM (i stress CALM) day you can fish Shark Point (this is the point out front of clovelly) - be careful and don't fish this place alone - you can get kingies, bream, trevally, squid, blackfish - etc
alasdair i have probably seen you out there - that is one of my favourite rock spots along the eastern suburbs
This should get you started.
gav