Example 1: On any given day, you can find me reading a book at Starbucks. I go there almost every day to study.
Example 2: There are lots of street performers on the Venice Boardwalk. If you go there on any given day, you'll certainly see something interesting.
on any given day is used the same way as any day.
This idiom can be found in Reading Horizons 1st Edition which is used to teach Reading/Vocabulary in level 6. For more information, please visit www.languagesystems.com