I'm a bit biased as Point Breeze is my hood and I want people to come this way and enjoy the area; but even if I didn't live a few blocks away, I'd make a point to frequent Point Brugge.
It's small and cozy with both table and bar seating. Nice selection of craft beers and a bunch of fancy schmanty cocktails available. Good selection of appetizers ranging from frittes to mussels to cheese plates.
I am not a huge fan of mussels but if you are I challenge you to find a better place than Point Brugge for them. This is their specialty and many of my friends have been unable to order anything else on the menu because they just can't stray from the delicious mussels (served in a nice sauce with a good helping of bread for dipping). Personally, I like their pasta dishes and recently had a butternut squash gnocchi.
Point Brugge is full of charm and good smells. I can smell the garlic sometimes from a block away when I drive through. It makes me happy.
My caution to you is that they don't take reservations and there is not a lot of seating so plan to come either early or to stand and wait at the bar. When it's warm out many people stand outside to wait and enjoy the pleasantries of Point Breeze.