As many other posters have stated, you are all good in your hotel! I vape in hotel rooms worldwide, never had a problem!
As far as vaping in airplane lavatories.... While some will not go off, please be advised, that most smoke detectors in the lavs are indeed the photoelctric type and WILL go off if you are vaping madly and blowing direct into the detector. I have set off detectors on my own aircraft testing this theory.
For those of you vaping in airplane lavs, please take a second between drags, and blow your vapor to the floor. If the sink is equipped with suction, which some are, blow your vapor down the drain. Setting off a lav alarm is a real pain in the A** for us flight attendants. It causes a lot of unnecessary paperwork, explanations to the flight deck, and they can be a real ....* to turn off sometimes! ;-)
Safe Travels!