RItz1024 and seremify007 are both on the right track, the
UBank USaver currently has the highest savings rate at 6.01% on the condition that you dump a min. of $200 in your account every month. While UBank is backed by NAB, UBank has no physical branches and all inquiries are done via phone and online banking. BEWARE, customer service is almost non-existent, but that's the price you pay for a high interest rate these days.
If you want physical branch access, I'd suggest the
ANZ Progress Saver (5.76%) or
Commonwealth GoalSaver (5.50%). Both work in a similar way as the UBank USaver where you have to dump a minimum amount every month ($10 for the ANZ Progress Saver and $200 for the Commonwealth GoalSaver). Note that if you don't meet these conditions for a particular month, your account will revert to the low standard rate for that month.
Note that rates for savings account are generally low at the moment. If you have a bit of money ($5000+), I'd suggest opening up a term deposit instead.
Check out the top Savings accounts here
Cheers