Short answer — mainly in Kuala Lumpur’s luxury malls and a few regional malls/districts. Top spots:

• Pavilion Kuala Lumpur (Bukit Bintang) — flagship designer stores and Fashion Avenue for luxury labels. (zafigo.com)
• The Starhill / Starhill Gallery (opposite Pavilion, Bukit Bintang) — ultra‑luxury boutiques and watches/jewellery. (en.wikipedia.org)
• Suria KLCC (at the Petronas Twin Towers) — big international designer names in a central, tourist‑friendly mall. (en.wikipedia.org)
• The Exchange TRX (Tun Razak Exchange) — new high‑end retail precinct with Seibu department store and many premium/first‑in‑market boutiques. (trx.my)
• The Gardens Mall / Mid Valley (Mid Valley City) — quieter, upmarket mall with premium brands. (eguide.com.my)
• Bangsar (Bangsar Village I & II, Jalan Telawi) — neighbourhood boutiques and local designer stores — good for independent labels. (timeout.com)
• Publika (Solaris Dutamas) — hub for local designers, pop‑ups and concept stores (good for Malaysian labels and unique pieces). (timeout.com)
• Penang: Gurney Plaza / Gurney Paragon / Queensbay Mall — the island’s premier malls for international and premium brands. (en.wikipedia.org)
• Johor Bahru (City Square, Komtar JBCC, Paradigm Mall) — convenient for shoppers from Singapore and carries a mix of mid‑to‑upmarket brands. (singsaver.com.sg)

Quick tips:

• If you want global luxury flagships (Chanel, Louis Vuitton, Gucci, etc.) head to Pavilion, Starhill, Suria KLCC and TRX. (zafigo.com)
• For Malaysian designers, indie pieces and pop‑ups look at Publika, Bangsar and selected concept stores in the malls above. (timeout.com)

If you want, I can: suggest particular stores or designers (international or Malaysian), map a shopping route in KL, or list where to find watches/jewellery or luxury beauty boutiques.