The Cat Museum is exactly what it sounds like: a museum devoted entirely to cats, housed in the Kuching North City Hall building on a hill northwest of the city centre. The collection covers cat symbolism in ancient Egypt, Japanese cat culture (the maneki-neko lucky cat is well represented), European and Asian cat art, cat-themed stamps and coins from around the world, and the specific cat sculptures and imagery of Kuching itself. The taxidermy section includes some Bornean wild cats.
Whether the Cat Museum is for you depends on your tolerance for its central premise. If you embrace it, the museum is genuinely interesting and offers real insight into how the cat-city identity of Kuching developed. If you are sceptical, it is a quick visit. The building is on a hill with good views over the city, and the drive out is a chance to see residential Kuching rather than the tourist centre.