And boy, did I have to think how to phrase that title so it made some sense!
I’m looking for things like Shakespeare’s “A Midsummer Night’s Dream” and “Beware the Ides of March.”
Any others?
Anything with the word ‘midnight’. Midnight Hour, Midnight in the Garden of Good and Evil, etc.
“High Noon” works, too.
“How Summer Day” by It’s a Beautiful Day.
“Eight Days a Week” – the Beatles
“A Hard Day’s Night” – the Beatles
“Five O’Clock World” – The Vogues
There are many songs which have days of the week in them: “Stormy Monday,” “Tuesday Afternoon,” “She Gets Paid on Friday,” “Saturday Night,” etc.
Anything involving the full moon, the full moon being the middle of the lunar month.
Middlemarch.
Spindoctors
What time is it?
4:30
It’s not late,
It’s early, early, early
25 or 6 to 4
Includes everything from 3:34 to 3:35
I think you misunderstood the OP’s request. 
Half a Life, V.S. Naipaul.
Billy Joel’s The River of Dreams features the phrase “In the middle of the night …” lotsa times.
So many, in fact, that I thought the song was called “In the Middle of the Night.”
The Moody Blues’ “Tuesday Afternoon” is in the middle of the week.
New moon would also qualify.
Anything with “high tide” or “low tide” in it.
some phrases:
“middle-aged” and “midlife crisis” referring to a person’ life
“The Middle Ages”; see also “medieval”
“half past” referring to a time, 5:30 = half past five
“midterm” for an exam halfway through the grading period.
a “semester” is half of an academic year, so the “semester break” is the middle of the year.
“hump day” (generally Wednesday) is the middle of the work week