Thu Thuy Tailor on Nam Ky Khoi Nghia st or Co Lang Tailor on Nguyen Van Thu st are my recommendation. They're not the biggest but they works for some generations, for a long time so they'll make your ao dai carefully.
Some other modern and famous tailors are: Sy Hoang Tailor (opposite the Reunification Palace), Cham Khanh Tailor (Nguyen Dinh Chieu Street, District 3), Lien Huong tailor (Pasteur, District 3)...
I hope that it can help!