The closest view spots "White Sides" and "Freedom Ridge", 11 and 13 miles away, were seized by the government in 1995 and are no longer open to the public. The closest view spot now is Tikaboo Peak, about 26 miles east of the base. Getting there requires some moderate mountain hiking.
There are other view spots, like Reveille Peak north-west of Rachel, from where you look right down the two runways at Groom Lake. But that spot is over 45 miles from the base and you need good binoculars and a very clear day to see any kind of detail.