Summary: The best day for posting to Instagram, generally speaking, is Thursday. The best times any day of the week are 2 PM and 3 PM.
Our Internet friends over at Hubspot recompiled the information from a Sprout Social study that is also available via link below. In general, between 2 PM and 3 PM CDT is the best time to post for optimal Instagram engagement. This can change based on the day of the week and what industry is posting. The best day to post on Instagram is Thursday. Thursday has engagement at 3 PM, 5 AM, 11 AM, and 4 PM. Check out the Hubspot article below and the original article from Sprout Social also. Thanks for the clicks!
https://blog.hubspot.com/marketing/instagram-best-time-post
https://sproutsocial.com/insights/best-times-to-post-on-social-media/#times-ig