I use Coinspot. It works well with an Australian or New Zealand bank account, and they gave me 3rd tier verification in 48 hours, and called me on the phone to ask some questions to get it done faster.
I tried Kraken, and managed to get Tier 3 verification, but then discovered the only way for me to deposit there was through SWIFT or writing a check, which takes days.
With Coinspot they use Polipay to connect to Australian bank accounts for instant deposits. Withdrawals are slower, but are processed every Tuesday.