You can find out about the history of Kuala Lumpur with a trip to Masjid Jamek Kampung Bahru Mosque. Amble within Chinatown or visit the shops in this vibrant area.
If museums are on your list of things to see, you might want to browse the collections at National Art Gallery in Titiwangsa. It's also full of great shops and restaurants, so you can spend the afternoon having a wander. If you want to see more of the museums in Kuala Lumpur, Petrosains Science Discovery Centre and Biomedical Museum aren't far.