Can foreign navies sail close to us coast?

Answer 1

Absolutely, as well as visit American ports when invited, or under certain emergency circumstances. Vessels of countries who are hostile to the U.S. must sail outside territorial waters, unless specifically given permission by the U.S. to come closer or into port. Of course with submarines, it's of course a different story, but it's still not that easy to approach the U.S. without being detected.

Known enemies or rivals of the United States whose naval vessels sail near U.S. shores are usually closely monitored by U.S. Navy warships and aircraft, though since the Cold War ended, they've gotten a bit lax at it. A Russian fast-attack submarine was able to slip into the Gulf of Mexico without the U.S. knowing about it until it was actually there - 20 years ago, that wouldn't have been the case.

Iran has recently rumbled about its "navy" sailing near U.S. shores. That's actually not a bad thing - it's much easier to sink enemy vessels when you know exactly where they are.