I recently noticed that our outside wall has a wet looking spot around the faucet.
I tried looking in the wall at the pipe (from the unfinished basement), but
Is there anyway to easily diagnose if there is a leak? There is a little bit of clearance around the pipe hole, but not much.
I have seen copper pipe have small pin holes on several occasions. If your pipe is copper and in contact with the cement this may be the cause. The only way to repair is to replace that section of pipe. When I do this kind of repair I make sure to use thick wall copper because it will last longer than thinwall.
If you live in a colder weather climate (though your picture indicates that you probably don't due to plants showing at this time of year, and it's not a freeze-proof sillcock), you may have an inside shutoff valve to that outside faucet. If you do have an inside shutoff valve, you could turn that off for a couple days and see if the dampness reduces or disappears. If it does, that would indicate that the faucet plumbing is the culprit. If not, look elsewhere.
Though the dampness all the way up to your siding would indicate that the faucet itself may not be the culprit, especially if you don't see any direct signs of water either on the inside or outside, and dampness might not typically run against gravity that far unless it's really flowing. Is there any plumbing in the walls above that location that might be leaking down? Bathrooms or showers/tubs that may be leaking into the floor and running out? A window that might allow water to get behind the siding and drip down to the foundation? Roof or gutter issue allowing water to run down behind the siding in that location?
If you have access to the inside of the wall put up some cling wrap on the wall. Relatively quickly you should see where water is leaking. You can do this above, under, and to the sides of this faucet. If you wait too long to look at said cling wrap, it could all be wet.
Also it wouldn't hurt to dig a foot or two down on the outside and create a temporary well. If you do this three foot across on the outside and 18" down you can then view what the wet concrete looks like in a week or so. If it looks the same you know that your wet concrete is from an indoor leak for sure. If the wet area keeps traveling down to the well line it could also be excessive water at that spot on the outside being trapped there and wicking upward.
Water doesn't flow uphill so I would look in the wall directly above the sill cock
