Easily the best duck over rice (kao na pet) in HY is at
Paeatoy Restaurant
Thanom Niphat Uthit 3
From the center, it's past, and on the same side of the street, as Hatyai Central hotel, just after a small stationery shop. There are two large Chinese temples on the opposite side of the street. It's before the Sakura hotel.
The stewed pork (kao na moo) is also delicious. There is a full menu of standard Thai dishes, almost all are B50. Portions are very generous. There are "pointing enabled" (if necessary) photos of the dishes on the wall.
The restaurant is clean and air-conditioned and the hosts are kind and attentive. My wife and I eat there regularly.