I swear by my Tilley hat. I got it about 15 years ago and it is still going strong, I wear it fishing, hiking, anywhere. It covers the back of my neck and has a "secret" compartment where you can put some basics, like ID, a couple 20s, and if needed shirt-pocket survival kit.

It isn't waterproof, but it dries quickly and a simple baggie will protect whatever is in the compartment. I use the chin strap if I'm out on the water, so it has never fallen or blown off.