L-glutamine should be taken on empty stomach b/c it competes for absorption w/ other amino acids. Therefore you have to take it on an empty stomach. It's primary use from the study Anthrax presented is as an anticatabolic agent. Therefore, if you take before breakfast and you don't do cardio or weights, you basically waste it IMO, unless you're looking for a faster recovery. Best time IMO to take it is as others have pointed out, right before you hit the gym, and before bed (and again on empty stomach). Right after the gym you should have your post workout shake, at this time your muscles are starved of nutrients and L-glutamine will not replenish them. You need more than L-glutamine. You could however take the L-glutamine in between your post workout shake and your solid meal. Once you have replenished your muscles w/ the necessary nutrients it needs to grow, then think about the glutamine.
If you have glutamine peptides, you could take it w/ your post workout shake. But plain L-glutamine you can't. Glutamine Peptides have been proven to be 3 times more absorbable and they wont compete w/ other aminos for absorption.
good luck