For most scenarios I'd prefer to shelter in place. I'd only move to a different place if I thought I'd be better off there, which I think implies a rather local disaster. In that case I'd try to travel far enough to reach "normal" civilisation, and then check into a hotel or something. I'd rather spend several days doing that, sleeping rough meanwhile, than be a burden on the red cross centres.

This kind of question is really hard to answer in abstract. The weather might make a difference. So might the amount of warning I got, or the nature of the emergency, or what I thought everyone else was likely to do, or what the authorities are telling us to do.