Lau Ya Keng Foodcourt on Carpenter Street is open every night selling satay and other yummy food

The two earlier answers are excellent. Now, I want to add something else. Some bonus information! While in Carpenter St, look out for China St. Coming from the Main Post Office, China St is on your left. On your right, the continuation of China St, is Bishop Gate (Bishopgate) St. It is a quiter, narrower, shorter street than China St. There are a number of quaint small shop houses now turned into cafes and B & Bs. An old well used by the ancient Chinese traders is buried underneath one of those shop houses. That old well is the basis of the real history of how Kuching derived its name. In Mandarin Chinese, gu-jing means old well. Forget about the story of Kuching being the "cat city". That's just a touristy invention, a baseless fabricated story. Both China St & Bishop Gate St are worth strolling through.

I agree Vincent gave a thorough and complete answer