It appears that the duties of such a high-ranking officer would be mostly coordination of the fleet, administrative duties, paperwork, and reporting to their superiors. Soon after the Battle of Yavin, for a few years, the Death Squadron was mostly hunting down the Rebels. That consisted of a whole bunch of space travel with intermittent battles, during which the admiral would be on the bridge, giving orders and controlling ship movements and strategy. When not fighting, he was probably planning for the next battle and following up on leads as to the Rebels’ whereabouts, avoiding/reporting to Vader, or doing related paperwork. Basically, the position of admiral is largely desk work until an actual war breaks out.
I couldn’t find a proper list; unfortunately, there tends to be a lack of information on the day-to-day routines of officers, because battles are shown far more often. I hope you can work with the more general info without too much trouble!
~ Jacen