Hi Tara, I did this holiday last year and as far as I can remember we didn't have to hand over our credit cards in any of the hotels. However, as only breakfast is included, I suggest that you do bring your credit card if you have one, as it would come in very handy in paying for meals - or else you could just go to an ATM every few days. However, if you want to do the Grand Canyon trip (which I strongly recommend!!) you will probably need your credit card to pay for the flights etc - which cost £200-350 depending on which package you go for. I did the three-in-one (helicopter, boat and bus) and you have to fly up to the canyon from Las Vegas airport in a small 20 seater plane (I think this cost around £350 altogether). Hope this helps!
Best wishes,
Bob