- Terms of stay for children - children allowed?
- Size of Room
- Non-Smoking (usually non-negotiable)
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.