It is becoming very difficult to find a place that does not accept a credit card; but on very rare ocassion I still run into them.
Tipping is one time when it isnt terribly uncommon to be told you can not put it on your card (mabye 10 to 15% of the time) and that has to do with how the accounting system works there and the VAT tax - tips are not taxable income but if it goes on a card stopping the VAT process is extra work).
Sometimes credit card networks or the shop wireless goes down. I run into that about once a month.
I try and carry 10.000 forints in my wallet. As much of it in 1.000 forint notes as possible.
There are ATM machines all over town. Try and stick to a bank ATM for fewer fees, but in a bind it really doesnt matter much. Most bank ATMs are in dedicated building vestibules. Its not as common as it once was but thee are still those that require you swipe a credit card to open the door. Any credit card and I suspect any card with a magnetic strip on it will work. Then PUSH the door to go in.