The phrase "almost any day" is correct and usable in written English.
It can be used to indicate that something can happen on most days, but not necessarily every day.
Example: "You can visit the museum almost any day of the week, except for holidays."
Alternatives: "nearly any day" or "most days."
Almost any day of the week, you can catch a string quartet performing in New York.
A feel for the dimensions of the problem can be gained almost any day on the docks in Red Hook, Brooklyn.
Almost any day on the block, which is lined with red-brick row houses, men work on cars, children play basketball, an ice cream truck beseeches attention.
In fact, Mr. Warner said, your breath can be visible on almost any day in a New York winter and even in summer, if the air cools to 50 degrees after a shower and the relative humidity is high.
At the top of that hill, on almost any day in July or August, you can find Robert Wilson, the theater's sultan of slow (his stage crossings can take 20 to 30 minutes), presiding over an astonishingly animated beehive.
On almost any day in their careers, the Yankees would have preferred to have the slugging O'Neill swinging at a 3-0 pitch with two men on than to have the pesky Sojo batting with the bases loaded.
It's the Landmark Tavern, on 11th Avenue in Manhattan, on almost any Monday evening.
On almost any Sunday you will see the duo, along with their comrades Richard Lee and Lloyd Williams, trolling the aisles of the Garage Antiques Market in Chelsea.
IT might have been almost any Saturday night in the last decade: a string of tail lights blazing like coals in the blue dusk; the air resinous with the scent of chaparral where the Foothill Freeway ribbons along the slopes that cradle the city's sprawl; and the voice.
Most notable of these from 1990 onwards was Laptaria Enache ("the Enache milk bar"), a long, narrow, usually crowded loft above the national theatre, where he could be found on almost any Sunday night when in town, heading a changing quintet, Johnny Raducanu and Friends.
He has a church in Memphis, and almost any Sunday morning he is not on tour, you can go listen to him sing and preach.
