It sounds like you will be taking both lenses with you, but are wondering which you are more likely to be using most of the time, yes?
What do you intend to shoot that is candid and distant, and do you foresee yourself shooting more of that then scenery, landscapes, landmarks, and family photos?
Unless you are dedicating the trip towards distant, candid people photos to capture the culture and lifestyle of the location you are visiting, I would also vote for 18-55 because it offers the widest angles through to 'normal' focal lengths, which are used for most subjects. The low end of the 55-250 range, up to about 85, may be useful in certain cases, but not as much as the 18-55 range.
I rarely use my 70-300 on vacations or trips, unless I am shooting something pretty far away. I do use it though, so I always bring it along. But it definitely doesn't stay on the camera for long.
The way I see it is, if there is even one situation where I need the 70-300, it makes having it with me for the rest of the trip worthwhile. Good example was shooting Puffins from far away in Iceland; we could not get any closer to them, so it was long lens or useless shots. Actually that was one of the really rare occasions where I found myself thinking a longer lens would have been great. It's just me, of course, as many people who do birding or wildlife would definitely disagree with my sentiment on the rare need for a long lens.