If you want to give your credit card some exercise, head out to Gurney Drive in Downtown George Town. It's also full of great shops and restaurants, so you can spend the afternoon having a wander. Splash some more cash at Gurney Paragon, Pulau Tikus Market, and Gurney Plaza.
You can find out about the history of George Town when you stop by Dhammikarama Burmese Temple. Check out the shops and top-notch restaurants in this walkable area.