We use a bit of everything.
In general, we put most things on credit card and find that they don't gouge us on the rate or the conversion fee.
We carry US$ traveller's cheques and usually cash a few every trip at our hotel... it's nice that they don't expire so you don't have to estimate exactly how much cash you'll need this trip, BUT not so nice that we bought our last lot when it cost more to buy $US. Also, traveller's cheques are not as convenient because many retail businesses don't take them any more. Use them as your travelling bank, cashing enough for the day's needs but not so much you feel uncomfortable with your pockets full of cash.
We use the bank card as a third choice, because between the ATM fees and our bank's fee it's the most costly option but still not outrageous or impossible. We only use our bank card at ATMs because debit is really hit-or-miss in US retail outlets...sometimes it works, sometimes it doesn't.
Honestly, you can go crazy trying to figure out the absolute cheapest/best way to carry your money, and then realize you agonized over saving maybe $10 or $20.