The CSS below can be added to your child theme's stylesheet (CSS file) or via a plugin like Reaktiv CSS Builder or My Custom CSS.
/* Hide the venues dropdown menu on the events calendar */
select#ee-venue-submit.submit-this.ee-venue-select {display:none;}
Want to hide the events category dropdown instead and keep the venues dropdown menu? Try this CSS:
/* Hide the event categories dropdown menu on the events calendar */
select#ee-category-submit.submit-this.ee-category-select {display:none;}
References:
https://eventespresso.com/topic/venue-dropdown/