Within a few hundred light years.

That is the key to what he actually said, you just choose to hear 'There are no aliens....' and cut off the rest of what he said.

Based on what we have found in extrasolar planets I hate to tell you this but the chances for happy planets in the the Goldilocks zone has dropped a lot. We have discovered that gas giants are able to take up orbits far closer to the central star, thus removing the chances of small rocky earth-like bodies.

Further, we now know that our large moon is one of the key stones to the development of life on earth. Based on what we have seen of our solar system a one large moon to one planet system is a rare 'fluke' not the norm. If it was then each of the inner rocky worlds would have a large moon.

Given the billions of light years that the universe covers yes we are likely to find a few alien species that possess intelligence.

However we should temper that with the very real truth that it took billions of years for a technology using intelligence to arise on planet Earth. This reduces the number of potential viable worlds that could possess intelligent life.

Further, we possess the means already to wipe ourselves out, it appears that this ability would be natural with any species that manipulates tools (is technological) and it further appears that "war" is part of the nature of technology development. After all it is not peace time that has spurred the advance of technology in our species, but the needs of war that has pushed the development of new technologies.

With all of the negatives against intelligence, the reason why we are not picking up Sirian "I Love Lucy" shows is either because those worlds never spawned life all due to the lack of a large moon, or because the gas giants are inner system bodies. Or They are not advanced enough to broadcast TV... Or they advanced to the point of nuclear science and annihilated themselves, or they developed millions of years ago and as all species are wont to do went extinct.

With all of these factors in mind, Hawking's point makes perfect sense.