Locals rotate markets by suburb and day — you won't catch them all as a tourist, but these are reliable: Kampung Baru night market (Wednesday & Saturday evenings, near KLCC — Malay food, nasi lemak, ayam percik). Taman Connaught night market Wed night in Cheras — huge, chaotic, 30 min Grab from BB. Sri Petaling night market Tue/Fri. Jalan Alor is every night but tourist-priced and half the stalls repeat. Pasar Malam in various housing estates — ask your hotel which night is nearest. Go 7–10pm peak. Cash still common at stalls. Wednesday Kampung Baru is my pick if you only do one "local" market without leaving the city center far.
TTDI night market Monday — expat favorite, still feels local. Further out though.
Kampung Baru Saturday night was packed — nasi lemak, grilled fish, no English menus needed if you point.
Ramadan bazaars March–April blow every other market away if your dates align.