When booking hotel rooms on Agoda.com, my "go-to" website for hotel bookings, my key criteria would be
- Terms of stay for children - children allowed?
- Location
- Size of Room
- Non-Smoking (usually non-negotiable)
These are in no particular order of priority, though generally, location is the first, and size of room is next.
Hotels that do not accept children usually won't even turn up in the search results.
And yes, non-smoking is almost non-negotiable. I can imagine a situation where I have to get a hotel in that location and there are no other choice except for a smoking room, and I might have to compromise, but generally, no.
Sometimes, other consideration may become paramount, but generally that is the order of priority.