Antithesis, according to wikipedia is defined as:
a figure of speech in which an opposition or contrast of ideas is expressed by parallelism of words that are the opposites of, or strongly contrasted with, each other, such as “hatred stirs up strife, but love covers all sins” : his sermons were full of startling antitheses.
Robert Frost uses antithesis when deciding which road he wants to travel. He wants to travel both but realizes it's impossible. Frost says:
I kept the first for another day!
Yet goes on to say:
I doubted if I should ever go back.
He basically goes against what he’s thinking throughout the poem and finally makes the right decision after much thought.
One of the definitions of antithesis (in literary terms) is some passage in which opposite, or nearly opposite, ideas are both presented as truth.
So, in antithesis, the author gives us two ideas and says they are both true even though we know they can't really be.
So where in the poem does this happen? I'd say the whole second stanza shows antithesis. Let's look at it:
Then took the other, as just as fair,
And having perhaps the better claim
Because it was grassy and wanted wear,
Though as for that the passing there
Had worn them really about the same
Here, Frost is saying first that one path was better because it was less worn. Then he says that the people passing had worn them both equally. This fits the definition of antithesis.
Antithesis is a figure of speech in which contrasting ideas are juxtaposed by a parallelism of words.