US State waters
For the most part state waters extend for 3 miles from shore. The exception is enclosed or Internal waters such as Long Island Sound, Chesapeake and Delaware Bays etc. where State waters can extend to a median line between states. The Great Lakes are a special case, all of the bottom is State or Canadian lands.
In Long Island Sound this can be less then 1 mile up to about 11 miles from shore depending on the area. States control the bottom per their own laws and most States control wrecks under the Abandoned Shipwreck law. As for how old a wreck has to be, NY says 50 years, some other states say 100. CT has never passed any laws under the Abandoned Shipwreck law but does have a law about removal of any object embedded in state lands which the bottom of Long Island Sound inside of the State line is. For a wreck this seems to mean, if you can see it, you can take it. If you have to dig for it, it is State property. However, no State laws will negate any Federal laws or treaties that may pertain to a particular wreck such as sovereign immune wrecks.
One note on the Abandoned Shipwreck law, abandonment is no longer considered to have happened by the simple passage of time. If you can buy the salvage rights of a wreck from the insurer or direct descendent of the owner you will have a very good case to void the Abandoned Shipwreck law and any other State laws.
Now for the other waters
(I stole this from another site)
Territorial waters,
Or a territorial sea, is a belt of coastal waters extending at most twelve nautical miles (but possibly less, at the coastal country's discretion) from the mean low water mark of a littoral state that is regarded as the sovereign territory of the state, except that foreign ships (both military and civilian) are allowed innocent passage through it.[1]
A sovereign state has complete jurisdiction over internal waters, where not even innocent passage is allowed. Territorial waters extend up to 12 nautical miles (22 km) from the mean low water mark adjacent to land, or from internal waters, as per the 1982 United Nations Convention on the Law of the Sea. The mean low water mark may be an unlimited distance from permanently exposed land, provided that some portion of elevations exposed at low tide but covered at high tide (like mud flats) is within 12 nautical miles of permanently exposed land. Completely enclosed seas, lakes, and rivers are considered internal waters, as are waters landward of lines connecting fringing islands along a coast or landward of lines across the mouths of rivers that flow into the sea. Bays are defined as indentations between headlands having an area greater than that of a semicircle. If they do not exceed 24 nautical miles (44 km) between headlands then they are internal waters; if their entrance is wider, then that portion landward of a 24 nautical mile straight line that touches opposite low-water marks across the bay positioned to contain the greatest water area are internal waters. All archipelagic waters within the outermost islands of an archipelagic state like Indonesia or the Philippines are also considered internal waters.
Contiguous Zone
Control over a contiguous zone, up to an additional 24 − N nautical miles beyond the territorial sea, where the territorial sea is N nautical miles wide, N≤12, is permitted by a coastal nation to "prevent infringement of its customs, fiscal, immigration or sanitary laws and regulations". The United States invoked a contiguous zone on 24 September 1999.[2]
Conflicts still occur whenever a coastal nation claims an entire gulf as its territorial waters while other nations only recognize the more restrictive definitions of the UN convention. Two recent conflicts occurred in the Gulf of Sidra where Libya has claimed the entire gulf as its territorial waters and the U.S. has twice violently enforced freedom of navigation rights (Gulf of Sidra incident (1981), Gulf of Sidra incident (1989)).
Exclusive Economic Zone (EEZ)
An exclusive economic zone extends for 200 nautical miles (370 km) beyond the baselines of the territorial sea, thus it includes the territorial sea and its contiguous zone.[3] A coastal nation has control of all economic resources within its exclusive economic zone, including fishing, mining, oil exploration, and any pollution of those resources. However, it cannot regulate or prohibit passage or loitering above, on, or under the surface of the sea, whether innocent or belligerent, within that portion of its exclusive economic zone beyond its territorial sea. Before 1982, coastal nations arbitrarily extended their territorial waters in an effort to control activities which are now regulated by the exclusive economic zone, such as offshore oil exploration or fishing rights (see Cod War). Indeed, the exclusive economic zone is still popularly, though erroneously, called a coastal nation's territorial waters.
Note: Shipwrecks are not controlled under the UN definition of the EEZ
The continental shelf of a coastal nation extends out to its continental margin, but at least 200 nautical miles from the baselines of its territorial sea. The continental margin is defined by a series of points not more than 60 nautical miles (111 km) apart where the thickness of sedimentary rocks is at least one per cent of the height of the continental shelf above the foot of the continental slope, but not more than 60 nautical miles inshore from it. The foot of the continental slope is where the maximum change in the gradient of the seabed occurs. The continental margin cannot exceed 350 nautical miles (648 km) beyond the baselines of the territorial sea or 100 nautical miles (185 km) beyond the 2,500-metre depth, unless "natural components of the continental margin, such as its plateaux, rises, caps, banks and spurs" but not submarine ridges are farther out. The coastal nation has control of all resources on or under its continental shelf, living or not, but no control over any living organisms above the shelf that are beyond its exclusive economic zone.[4] Ireland has become one of the first countries to define its continental shelf in accordance with the UN convention.[5]
Pirate radio broadcasting from artificial marine fixtures or anchored ships can be controlled by the affected coastal nation or other nations wherever that broadcast may originate, whether in the territorial sea, exclusive economic zone, the continental shelf or even on the high seas.[6]
Thus a coastal nation has total control over its internal waters, slightly less control over territorial waters, and ostensibly even less control over waters within the contiguous zones. However, it has total control of economic resources within its exclusive economic zone as well as those on or under its continental shelf.
So, beyond State waters and on non sovereign immune ships it looks to be wide open. But, EPA or National park laws such as with the USS Monitor may be applicable to US citizens even beyond the 12 mile limit.