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.

Explanation:
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