Indeed, there is one tiny Alaskan island where you can see a tiny Russian island.
http://en.wikipedia.org/wiki/Diomede_Islands
But here's something that says more about what the relations between the countries COULD be.
Around Christmas time, Christmas Eve in fact, NORAD has a thing where you can track Santa's progress around the world. And SAC-Alaska has its own local version.
I worked as Live Van operator for KTUU, the Anchorage NBC affiliate and covered this story at least a couple of times. It was really neat to see these ancient air traffic control-looking panels. I even have a picture of myself sitting at one.
More impressive is the wall of the room which is covered in red stars. Each is a US intercept of a USSR plane. The plaque lists the date and type of airplane.
The public affairs officer said she was leading a tour of some USSR/Russian military people. One of them walked over to the wall and looked at it a while and finally pointed at one of them: "That was me".