When will the earth and/or solar system see direct effects of being in close proximity to a black hole?
The black hole at the center of the Milky Way Galaxy is some 100,000 light years distant. As best as astronomers can figure, we sit on one of the spiral arms towards the outer limits of our galaxy. It is estimated that our sun has about 6 billion years of life left in it before it explodes into a red giant taking out half of the solar system with it.
Now, the Milky Way Galaxy has been around almost as long as the universe had existed. In theory, some day all the stars of the galaxy will burn themselves out and after that, well, we just don't know.