As Romp said above, if you don't mind paying a reasonable amount (over $200 per shirt), you can get ready-to-wear shirts at P.Johnson tailors that look very nice, or you can pay a bit more and get made-to-order shirts there. Alternatively, Charles Nakhle in Parramatta will make you shirts for around the same price (over $200).
There are plenty of ready-to-wear online shirt places, some with bricks-and-mortar stores, too. Two that offer reasonable shirts at low prices are Charles Tyrwhitt (commonly abbreviated to CT around here) and TM Lewin. Please ignore Thomas Pink as their shirts are pretty much identical to TM Lewin and Tyrwhitt but they somehow manage to get away with charging about four times as much for no good reason at all. Both Tyrwhitt and TM Lewin have pretty much continual "buy 4 for $XXX" sales, where you can pick up decent shirts for $40 or $50 each. Their shirts are easily as good as shirts that sell for $120 - $160 or more in places like DJs.
If you like the idea of button-down collar shirts, have a look at Land's End in the US, as they make good quality, good value oxford cloth, button-down collar shirts.
As Romp also mentioned, there are now quite a number of places doing online, made-to-order shirts. Some of them are decidedly better than others. I haven't used any, but people here seem to have had good results from Luxire and Cottonworks, amongst others. Hopefully, some other people will chime in with their recommendations. Please note that ordering made-to-order shirts online might mean that you'll have to order one, or perhaps even two, cheap shirts first to work out any fit issues or problems with your measurements before you can feel confident in getting your fit absolutely right.