These are my favorites: I can’t pick just one! (But they are in order).
Season 2, Episode 6: Eye of the Beholder
Original Air Date: 11 November 1960
A young woman lying in a hospital bed, her head wrapped in bandages, awaits the outcome of a surgical procedure performed by the State in a last-ditch attempt to make her look “normal”.
Season 3, Episode 8: It’s a Good Life
Original Air Date: 3 November 1961
On an isolated family farm, a young boy with vast mental powers, but lacking emotional development, holds his terrified family in thrall to his every juvenile wish.
Season 2, Episode 28: Will the Real Martian Please Stand Up?
Original Air Date: 26 May 1961
Following a frantic phone call about a crashed spaceship, two policeman try and determine who among the passengers of a bus at a snowed-in roadside diner is from another world.
Season 5, Episode 7: The Old Man in the Cave
Original Air Date: 8 November 1963
In a post-apocalyptic settlement, the inhabitants’ survival is dependent on the advice of an unseen man living in a nearby cave. This dependence is tested when a band of soldiers descends on their town.
Season 5, Episode 4: A Kind of a Stopwatch
Original Air Date: 18 October 1963
A man is given a stopwatch that halts time.
Season 2, Episode 7: Nick of Time
Original Air Date: 18 November 1960
A pair of newlyweds stopping in a small town are trapped by their own superstition when playing a fortune telling machine in a local diner.
Season 1, Episode 22: The Monsters Are Due on Maple Street
Original Air Date: 4 March 1960
On a peaceful city street, strange occurrences and mysterious people stokes the residents’ paranoid to disastrous intensity.
Season 1, Episode 30: A Stop at Willoughby
Original Air Date: 6 May 1960
Tired of his miserable job and wife, a businessman starts dreaming on the train each night, about an old, idyllic town called Willoughby. Soon he has to know whether the town is real and fancies the thought of seeking refuge there.
Where I live, the next city west of me IS called Willoughby. I have only seen this episode once, but it IS believed to be filmed here near me.