If you want to eat Bak Kut Teh in the morning, may be you can go to Gurney Drive.
There are few coffee shop selling Bak Kut Teh, such as Kedai Kopi Song River, Carnation Bak Kut Teh, Food master, Zealand Bah Kut The etc.
Bak Kut Teh come with white rice or yam rice also taste good. You may also order some side dishes like fried vegetable, yew char kuih and bean curd.