Kek Lapis is a layered cake popular throughout Sarawak. You'll find it for sale everywhere you go in major cities, from coffee shops to street-side vendors. It has a rich buttery taste and comes in a dazzling array of flavors. Many flavors are run-of-the-mill (chocolate, strawberry) but I would recommend seeking out ones more unique to Malaysia (pandan is especially popular). Kek Lapis is generally not available with preservatives and has a shelf life of around three days, so if you are planning on bringing it home you should purchase it just before your flight.
The Mira Cake House in Kuching is dedicated entirely to Kek Lapis. If you're in downtown Kuching, you can hop across the Sarawak River in one of the ubiquitous water taxis (only 1RM) and find it in Kampong Boyan. After grabbing your cake, there are several food centers along the river nearby where you can grab a meal or iced coffee to go along with it.