When visiting the US we have normally booked a lot of things prior to travelling and then we carry cash and use the card for "splashing out" a little when we think necessary. We don't use the card to withdraw cash, as that's where the charges are higher. We divide the money so we are all carrying some, so that if we lose any, or it gets stolen, we will only lose part. If you carry cash, always get out a small amount of spending money for the day, so that you are not revealing a lot of cash when making purchases and make sure the other is securely fastened in a safe place on your person.

We have always felt comfortable doing this, but don't take this info as a recommendation, it is for you too decide how you want to go about things, and whether the bank charges are worth the extra security that come with them.