will space travel take place inside a sort of craft or, as suggested by K-Pax, a more exotic way of travellin

I would definitely not count on getting an answer you could believe here. It would be a pure guess.

To get to another star?

Designs such as Daedalus and Project Longshot involve actual craft to get to Barnard's Star and Alpha Centauri. Just about anything we are physically capable of doing - and can physically understand to be possible - involves some sort of craft. Anything outside of that is imaginary physics.

If you are referring to interstellar travel, I think you can count on any means of doing so looking very different from anything we now think of as a spacecraft. Since we currently don't know any technology that would enable such travel, we can't begin to speculate on what form it might take. One line of thought is that since you can't travel *through* space at or beyond the speed of light, we will have to find a way *around* space. Or maybe the answer is to evolve a metabolism so slow that a million-year journey is no big deal...

Something more exotic.

Nothing may exceed the speed of light.
This makes linear interstellar travel via some form of craft impracticable/ too slow.

Something "more exotic" is required.

Who really knows at this time, how far we will advance. Perhaps someday we will be able to instantaneously teleport to anywhere we decide too.