Following A Lead
Your next dead drop is very easy to find. It's a barrell behind the statue just to the right of the main gate as you enter Anvil. When you check, it's empty. Good. You just need to sit back and wait for whoever has your orders and confront them about it. So back off a little way and wait. Shortly, a Wood Elf will come wandering over to the barrel and stand there for a while. When you activate him, he'll confess the whole thing.
A "robed man" paid him to put the orders in the barrel. All of the conversation topics will get you the same answer: he thinks the robed man lives in the basement of the lighthouse, there are some really bad smells coming out of that basement, and you should go talk to Ulfgar Fog-Eye to get the key. If you open the barrel, you'll find your new orders, but no money. That's right, the little fetcher decided to keep your payment. If you want your money, you'll need to either pick his pocket or kill him to get it (he stops being essential after he 'fesses up). Since he's Morvayn's apprentice and might be needed later for buying/selling/repairing weapons and armor, I don't recommend killing him (not to mention the problem of the city guards standing a few yards away). But if your Sneak skill is good enough, you can nick your gold pretty easily (as well as whatever gold Enilroth would normally have - call it penalties and interest).
Your new orders point you toward a prostitute named Arquen, but don't tell you much about her location. Don't bother looking for her; you'll meet her soon enough. Your target for the moment is Ulfgar Fog-Eye. Just follow your compass. Most of the day he is actually at the lighthouse, but he does go to the chapel every morning for a few hours. When you talk to him, don't use the "[Say Nothing]" topic. It only makes him mad and will cause him to attack you. Either of the other two topics will get you the key you need.
Once you have the key, head down to the basement. It's full of food, containers and corpses (which is undoubtedly the source of the smell that everyone has been mentioning). There is a "Crazed Dog" in the second room that shouldn't be a problem at this point in your career, but no other living things. There are, however, two important items: a head sitting on a platter surrounded by candles (might be useful later) and a journal that you will need to read. Someone in the Black Hand wants revenge on Lucien Lachance and the Night Mother for the murder of his/her mother many years ago. The head is apparently the mother referred to in the journal. Once you have read the journal, your job is done and you can go meet Lachance at Applewatch.