Most of the sights of Kuching have to do with its colonial past as a major industrial trading port. With that in mind, the place to start is probably the waterfront area. Across the river is the rather fantastical structure of the Sarawak Legislative Complex. The building stands between the old Fort Margherita and the Astana. The waterfront development included a restoration of the old Chinese courthouse, turning it into the Chinese History Museum. Near the other end of the waterfront is the old Square Tower, which once served as the prison.
Behind the Square Tower is the Courthouse complex which is now used as a tourism center. Moving further away from the river, behind the courthouse is an old commercial building now being used as the Textile Museum. Continuing along further away from the river, perched on a small hill is the impressive Sarawak Museum complex.
Every corner brings an interesting new sight in Kuching
Kuching has several ethnic areas as well. The local 'Chinatown' is along Carpenter Street and there's also an India Street. On the subject of streets, the Main Bazaar Road is definitely the place to go for souvenirs and local handicrafts.
See the map page for a layout of the city and where all of the above sights are locates.