All the people who are jumping in and saying TIT should know this is the case in the USA as well. Due to the complex pricing..yield demand dynamic pricing..corporate discounts..bulk booking rates.. and individual Hotel cannot often offer the best price since they have to go with their price list. I had her telling telling me to book online to get the best price. This has happened several times when I booked in the US.
Actually it's an interesting idea. My bank in the USA pays the withdrawal fees. The exchange rate is usually good. So it's worth checking the difference overall. Wise charges fees and exchange rates seem similar to what I get with my ATM withdrawals.