Will commence European holiday (2019) in Budapest, however as many reviews state a debit card is useless at ATM'S, and it is very difficult to get HUF notes in Australia prior to leaving, what can we do ?? Take Euro (cash),or risk having a debit card fail.
My answer is from experience only.
There are plenty of cash machines in Budapest, most offer HUF and Euros(always use HUF for better value).
My debit card has always worked in Budapest like it has anywhere else. In fact I now don't get HUF here in the UK before I go anymore as I always seem to get a better rate in Budapest. I usually get about 340HUF for £1 here but it's about 360HUF to £1 there and my card has no currency exchange fee.
I've used cash machines that are connected to banks and just the random ones that are connected to bars in District VII. Usually the rate is a bit better at the cash machines connected to banks (Hungarian banks not foreign ones).
There are also plenty of currency bureaus that still offer a decent rate, sometimes the same as the cash machines, you can use your card in there too to get money out or exchange cash.
ATM worked fine for me but you are right to consider if it doesn't which does happen depending on where your card is issued and complicated inter-bank networks.
Bringing EUR is a good idea. As HUF are also hard to get for me, I asked this question before travelling. As you can read from answers, they are even accepted directly in many places that cater to tourists. However, the rate is often quite poor but EUR can easily be exchanged for HUF at currency exchange outlets for a reasonable rate. In any case, it is always good for your to lookup the current rate yourself as a reference point to make sure that you are getting a good deal.
I am a little bit puzzled by why would you take EUR with you to Hungary when Hungary is not in the euro zone and very few places accept Euros as payment and at terrible rates. If you are afraid your bank card won't work (ask your bank first?), bring Australian Dollars and use a comparison site like http://valutavaltok.hu/valuta-arfolyamok?currentpage=0¤cy_id=AUD&box_search_open=0&box_search_open_date=&box_search_city_id=392&box_search_region=&language=en&orderby=buy_rate&orderby_direction=desc& to find whoever is giving you the most Hungarian forints for your Australian dollars.
I also suggest using a credit card to pay for stuff or ATM with a debit card for getting cash. But if you bring AUD, you might be better than converting it to EUR and then HUF. The rates at the moment ( https://correctchange.hu/ ) are 198.10-201.90, so around 2% difference between buy and sell price. EUR is slightly better, but you need an AUD-EUR conversion as well.