What are the modes of transportation at Kuching airport and what time the last taxi available?
Taxi's run all night - there is a surcharge after midnight.
You can also use Grab or Uber.
Your hotel may provide a pick up service.
It takes about 25 - 40 minutes to get into the city - depending on traffic.
I highly reccomend downloading and using the Grab app. It is way cheaper than the taxis and really easy. Uber is no longer in use.