I think you will enjoy Restaurant Eugene. It is absolutely my favorite place of its kind in Atlanta. I think 13 year old foodies will be very welcome there and will enjoy themselves.
I would recommend against Blue Pointe. I haven't been knocked out by it. Plus, I wouldn't consider it particularly fun nor relaxed. I would suggest you check out the boards for the opinions of others if you haven't yet. I think the posts are probably pretty mixed.
The Buckhead Diner is a great suggestion. You may also want to consider Kyma for good Greek food. Could be a fun, new and interesting experience for 13 year old foodies. Having said that, it isn't as relaxed as Buckhead Diner.
Let us know what you chose and how you liked your meals.