Generally Penang is having a shrinking market where one mall opens the other dies. Some of the die hard shopping centers or complex list are:
1. Island Plaza: target to be high-end shopping center where you can still get Cold storage, FILA, Mango/MNG, Coffee Bean, Starbuck, Super Tanjung (where you can find branded stuff like East India boutique, Nike, Vince, etc). Many store from 3 floor onwards are closed/shut down due to economy downturn.
2. One-Stop Midlands Park Centre.: mid end shopping center, where you can still find some goodies there like cheap DVD (popular movies-RM 15 for 7 movie in one DVD, Hong Kong/Chinese series-RM 4 per DVD with 10 chapter in one DVD, etc), cheap software installation disk at the 7th floor (RM 8-10 per DVD installation disk), Siam/Thai hawker food, karaoke center. Many store are closed there at the middle floor (3rd-5th floor).
3. Komtar: Forget it, I can't see much there for shopping (it was good during 1985 - 1990, WAS/not now a high end place for shopping). I would rather shop in Prangin Mall and GAMA if I were there. Some that worth going is ACE travel agency if you were to consider traveling from Penang, Boon Hua Hawker center where recommended hawker is it's wan tan mee stall and tasty "teh-peng", and gold seller shops around for bargain. Yes, if you like sewing you can get some of the raw material around there a well.
4. Penang Plaza: Well you can still get Giant hypermarket, Guardian pharmacy, RM 30 haircut in there. Shops that worth going around there are in New World Park that opens until midnight starting from noon(enjoy hawker food, Old town restaurant, Starbuck, foot message, bah kut teh). Enjoy herbal tea (sour tea/"koh teh" in hokkien) near NETCITY.com.my a popular internet cafe.
5.Kompleks Bukit Jambul - Used to be a popular midend - highend shopping center 7-8 years ago in Bayan Lepas area, well not now. Would rather choose to go Sunshine Square if I were around there. Some of the place that worth going would be the Hong Kong restaurant nearby.