The anti-siphon cap on top leaks a lot of water when the faucet is turned on. I removed the black plastic cap and unscrewed the white plastic "plug" and found the small (1/4" - 3/8"?) washer has rotted and split. First choice would be to just replace the washer, second would be a repair kit.
How do I get a suitable replacement?
Take these parts with you to a hardware or plumbing parts store.
Not the Big Blue, Big Orange, or Big Green stores, if you're in the US & Canada - get a real "mom & pop shop" type hardware store. You might get lucky at the big box shops, but selection and helpfulness will be better at the small shops.
You're looking for a rubber washer of the same material, size, and shape. Test-fit them until you find a good one.
That looks like a Plumber's Choice brand anti-siphon frost-free outdoor faucet. See if you can find who sells that brand around you, as they might have the parts. However, note that most of these have a threads at the other end of the pipe (the side inside of your house), so that you can unscrew the whole thing, get a new one for $40, add $0.05 worth of Teflon tape and be done with it for another 20 years. Your choice.
