Is it permissible to use hotel cups for drinking water or juice, knowing that the hotel serves alcohol and these cups may have been used for drinking alcohol and then washed, even though they appear completely clean with no trace or smell of alcohol?

The default status of all objects is purity. This is a testament to the ease and leniency of Islam. The default status of vessels is that they are pure and permissible to use. The vessels of all disbelievers are pure if their state is unknown, even the clothes that touch their private parts, and similarly, what they dye or weave, and likewise the vessels and clothes of chronic drunkards. Therefore, these cups are pure, and you are permitted to use them.