I think some of the smaller banks, e.g. Bendigo Bank, have decent credit card deals. Or try the credit unions.
As a result of a multiplicity of irritations, including Qantas no longer accepting points transfers from American Express, I changed my credit cards - to Westpac Qantas Mastercard and W'pac Qantas American Express. Westpac is definitely not my preferred bank (old irritations!), but offered the best deals for what I wanted, so I didn't change my bank - they're all equally crap so I stayed with the NAB. There's an annual charge - $75. Interest rate on purchases is 17.74, but I'm very strict about paying it off.
When I tried to cancel my existing credit cards, both the bank and American Express have almost begged me to keep the card for free, i.e., no annual fee. No points accrual, though.
Perhaps if you try to cancel your bank will do the same.
I don't know if there's any winners with banks (apart from banks). Occasionally the Sunday papers will do a bit of a comparison in the finance section.
Good luck!
PS - as Robert said - not even shoes