Travel+Leisure portraits Anan’s Peter Cuong Franklin and Å By Tung’s Hoang Tung and mentions a couple of other fine dining restaurants.
Having been to Anan twice I’ll add some of the other places to my list.
Phu My Hung is one of my favorite places in Saigon. It has so many nice corners, a lot of soothing greenery 😉 and walking around the area is pure pleasure.