They make some awesome mini camping trailers these days. There are some that can be pulled by a small car and some that even pull behind bicycles. Failing that, and depending on what your surroundings are I guess there aren’t many better options. Try to take refuge in buildings or other structures along your route. Depending on the circumstances though, that could be asking for trouble.

If not tent, how about a sleeping bag under a tarp?

going to a friend or relative
going to a hotel or rental cabin

As a member of my local CERT, I have trained and drilled on plans for running a shelter.

Our shelter rules are simple but strict: no pets of any kind, no violence of any kind, no drugs or alcohol, and keeping reasonable quiet hours. That’s it — we ask for names as people enter and leave, but we don’t check IDs and we don’t keep anyone from leaving who wants to.

While FEMA administers some aspects of the CERT program nobody on our team has ever seen or spoken to a FEMA employee ever; as one of the leaders on our team I would know.

Our communication with our state’s emergency management agency is very limited. Our county’s emergency management agency can request for our team’s activation and to implement our sheltering plan, a situation which has happened.