Typically, hotels around the world will be keen to follow local/state indoor rules on smoking, especially as the price for the room increases. Most hotels will have some sort of specific policy around vaping on the premises, so asking the front desk before or during your stay about where you can vape would be a wise move. A good rule of thumb, however: if you can't smoke there, you probably shouldn't vape either.
Keep in mind as well that it's still possible for vapor to set off smoke alarms, especially the high tech ones installed in high-end hotels—once one goes off, ALL the alarms in the hotel are designed to go off as well, no matter what time of day (or night). And in addition to the sheer embarrassment as you start your walk of shame down to the lobby, needlessly setting off the hotel's fire alarm can incur a fee (~$200-$1000) on your final invoice. Ouch...
Ranches / Hike-In Lodging / Bed and Breakfast
When considering the small quarters 15-50 people will be sharing while resting their feet during their respective vacays, it's no wonder that the vaping policy for these types of lodgings is really dependant on each location. Some places treat smoking and vaping the same, some are more relaxed with vaping, and some disallow both from the grounds entirely, so consult the lodging's management before clouding up your room.
In the case of group hostels, the quality of the housing and/or occupants may make or break your most excellent vacation experience, so choose wisely! You may be in luck, as some of your fellow travelers may even vape themselves (depending on your location), so if you're running low on vaping supplies, you can always ask your neighbors and roomies where the closest vape shop is.
And make sure to keep a close eye on your belongings while you're there, just in case. If you're provided with a locker on the grounds, feel encouraged to keep your valuables—which includes your vape, obviously—locked up tight and away from prying eyes.
Ask ahead of time! Each owner will have often have more detailed rules for the house beyond the simple "Smoking Allowed/Not Allowed" note they're able to post to the site.
Some owners may be cool (they may even vape themselves), but some owners may not be as vape-educated as others, so they may send you outside (no biggie). Either way, don't be afraid to bring your vape to your new home away from home.
When funds are running low, prospects are dim, and you're more than a mere walk away from home, you may need to cutback on your travel expenses,
and an easy way to reduce your lodging expenses is by joining a couchsurfing service that will connect you with locals offering cheap housing for a night or two.
While this service is more often a lifesaver than not, you'll need to stay aware of your belongings at all times. There are several reports of someone having their vape gear being stolen while they were residing on a stranger's couch. Keep in mind, though, that most of this pilfered vape gear weren't even stolen by the host, but by an unrelated visitor of the house, so while you probably won't have to sleep with your mod under your pillow, you probably shouldn't leave it behind when you head out the door to explore the city.