My pack says "before workouts", as its an "Athlete Series". I personally have taken this statement as meaning on an empty stomach. I am also sure I have read somewhere that its generally best to take amino acids on an empty stomach.
I personally dont go out of my way, either way, and my last Uric Acid levels were comfortingly high (above the range the lab considered normal). It was originally below the normal range before I started.
I take about 2000mg / day of Inosine, split in two doses.