stopover-rates exist (to my knowledge) for most international airline-programs. They typically include transfers airport-hotel and are often reasonably discounted. I sometimes use the programs of Thai Airways.

As I/you have typically to book them together/in-connection with your ticket and with your airline, there is no need to show your airline-ticket at hotel-check-in.

But sometimes, on weekends, I get better promotional weekend rates from the hotels themselves.