They haven't decided yet which hotel to stay at.
这一句which hotel to stay at
=which hotel they should stay at
=they should stay at which hotel
stay后接at才能接宾语的.
Animals will commonly use force,or a show of force,to decide which will stay.
这一句which是充当will stay的主语.所以,stay后面不接宾语,也就是说,不用加at