You can purchase online through Hyatt.com but it takes you to a third party site which... can be a little sketchy if your credit card company does not think the site is secure

(long story short, tried to purchase online, saw charge pending on CC, Hyatt's third party gift card company cancelled the order because my cc company would not verify my address to them, then third party site said I could still purchase card online but could only do so using a new link they emailed to me that did not contain Hyatt in the URL. Thus began my quest to find a nearby property with physical cards)