It depends what you want to test. You can keep an eye on your fasting levels by testing immediately you get up in a morning, you can test just before bed to see what the whole day has done to you, or if you want to test different foods to see what they do to you, test immediately before eating then 1 hour and 2 hours after starting to eat. The testing foods bit is the best way to learn what you can and can't eat.
a small low carb late night snack might help reduce your morning sugar levels. The reasoning being you are shortening the number of hours without food overnight and duping your internal diabetic control centre in relation to its workings re length of perceived starvation.