Royal Sonesta is great place to stay, or the Hotel Montelone (has a carousel bar that is always spinning.) Those are both in the heart of the French Quarter. Theres the W right next to Harrahs Casino which is contemporary and nice. Harrahs has very nice rooms as well. All areas are pretty safe. If you stay in quarter just stay on the main streets and dont wander too far.
When you go to visit Brian you will cross GNO bridge and go to the west bank to get to the Turn. You will have to take Gen. Degaulle to get there. I wouldnt bother stopping anywhere on that stretch, I grew up in that area and it has gone downhill lately. Just go straight to English Turn. Its a great golf course and area. Have fun and enjoy your lesson and stay in NOLA. If you are interested in hitting the night life, I have some suggestions for that too.