The best way to find out what food you take can affect your blood sugar value is to do your own "experiment" at home. Test your blood sugar value before meal. Take another reading 2 hours after you have consumed the food. Use one of those home kit for blood sugar testing (e.g ACCU-CHEK, Omron, Sinocare, etc). It is tedious and requires discipline. I have developed it into an "art". I weigh my dry pasta before I cook it so that I control the portion size. It's not just the type of food you eat but also the portion size that can affect your blood sugar level.
The HbA1c value only gives you the average blood sugar value for the past 3 months (your 6.0 to 6.2 values are very good). Some food release sugar to your blood faster than others (Glycemic Index), which you have to be aware of (e.g. refined sugar, etc). As a diabetic, you should avoid this type of food as sudden spikes in blood sugar level over time can damage small blood veins especially in your eyes.
It doesn't mean that as a diabetic your cannot enjoy your food. Eat everything in moderation and some type of food less frequently than others.
Good luck in your effort to control your diabetes.