I'd like to dive a U-boat (no penetration) sometime next year as I have always been fascinated by WWII history. I have done some research online and found that the most accessible ones are U-352, U85, U701, and U-853 (am I missing any?).
I have been on 3 of the 4 - U-352, U-701, U-85.
As many of the comments suggest, the U-352 is probably the easiest, and potentially most enjoyable dive of those three. It gives you a combination of depth, usually (not always) good visibility, some pellagics swimming around. It is s shorter dive, because of depth, but you are TOUCHING HISTORY, as you are with all three - they were sunk in hostile action.
The U-85 is shallower (~85 feet), colder (Labrador current rather than the Gulfstream) and the viz is not quite as good. In some ways it is a more interesting wreck I have dove it wet (5mm with 5mm hooded vest) and was reasonably comfortable, and I have dive it dry (my preference). It is not as frequently visted by the larger operators (Olympus and Discovery), but you can get a charter out to it. Some 30+ years ago, Jim Bunch spent what amounted to several years diving the boat, and actually cleaning it out, and wrote a book about it (
A Shadow in the Sea: Germany's U-85). I have heard Jim speak about it a number of times, and - frankly - what he did, when he did it, is absolutely remarkable. He subsequently 'updated', or at least expanded, the topic in a second book (
U-Boats Off the Outer Banks: Shadows in the Moonlight) which is a more general history of Torpedo Alley.
The U-701 is my personal favorite, but it is also the hardest to get to in terms of boats running out to it, and the most unpredictable in terms of conditions. It is similar to the U-352 in terms of depth, maybe a few feet deeper. I have been on it when storms had essentially cleared all of the sand away, and the boat was uncovered, there was little / no current, and the viz was great. I have also been on it when it was hard to actually see much of the boat because of covering sand, the current was ripping, and the viz was low. I don't know which operators go out to it with any regularity - I have gone out of Hatteras when I have been on it, but the number of Hatteras operators has shrunk over the years. In good conditions, it is a great dive.