A lot of people will tell you the days of an easy catch in the Perth metro area are over... those people are most likely fisherman who are having a lean run. There are plenty of spots around Perth where you can hook up some excellent fish, here are some of the best.
Blackwall ReachBlackwall Reach is possibly the best spot for fishing in Perth. Due to it's location close to the Swan river mouth and the deep water you get all the typical river fish, plus some big salt water species.
You can fish from the rock wall or by kayak, get your baits and lures 10 metres from the wall to hit the big drop off, this will also help avoid the blowies. It's good any time of day but your best bet as always is to get there just before sunrise.
The list of regular catches from here is big. Flathead, Giant Herring, Black Bream, Tarwhine and Snapper are most common. There have also been reports of Bull Sharks and Dhufish up to 20kgs reeled in from it's depths!
North Mole, FremantleI haven't fished at the North Mole but have heard more than enough positive feedback from friends and the fishing community.

The North Mole
The popular diving spot is frequented by a variety of fish including King George Whiting, Herring and Skippy. Reports have also come in of Salmon, Bonito, Sambos and decent sized sharks and squid.
South Rock Wall, HillarysBoasting plenty of room for everyone to share, the southern rock wall is a favourite amongst locals. In the mornings the water is calm and crystal clear meaning you can spot schools of fish from a good distance.

Plenty of room for everyone along here
There is very little to get snagged on here so you can use smaller rods. From personal experience mulies on gang hooks provide the best results as this is a Tailor hotspot. Using bottom rigs and fishing until late evening also garner good results.
Besides schools of big Tailor you can also catch Whiting, Garfish, Herring, Squid and even Flounder. You do have to be watchful of the seaweed as the wrong sea breeze tends to wreak havoc there.
Two RocksTwo Rocks is a Dhufish hotspot at the right time of year. Most places you need to get out in a boat to hook up any demersal species but at Two Rocks you have the luxury of being able to reel them in from the beach.

Red marks off road access
You can catch and release at any time but if you want to take one home with you note that this is illegal from mid October to mid December to help increase their stocks.
You also have the chance to hook up big tailor (especially in the summer), rays and even sharks. Having a 4wd to access the best spots is desirable unless you fancy walking a bit, but staying just north of the marina can be quite successful as well. The beaches north of the marina have plenty of gutters and small reef areas to target.
Rottnest Island
As with all water based activities in Perth, Rottnest stands head and shoulders above the rest. Rotto will provide you with your best chance of hooking on to a good sport fish, spend enough time and your 95% guaranteed a catch at pretty much any of it's beaches.

The calm bays are perfect for fishing
Whiting, Herring and big Tailor are common and you have a good chance of hooking up rays and big Samsonfish - one of the best sports fish around (and damn tasty too!).
Fishing from the rocks, beach or boat are all highly successful, more often than not you just have to chose which ones to throw back and which ones to keep as you should always only take what you plan to eat.
For up to date info on whats biting and how to catch it check out Fishwrecked or the fishing section of the Sunday Times.