The Universe Within 12.5 Light Years

It should be a goal for Earth to send a probe to one of those stars. As the probe will be unmaned, a mission taking a hundred years or more is not out of question.

One issue with the latter is that tech is likely to advance fast enough that a subsequent probe launched a couple of decades later would overtake the first probe.

Regarding the former, various studies have been made and will certainly continue to be made: https://en.wikipedia.org/wiki/Interstellar_travel#Designs_an...

Exploration of the Very Local Interstellar Medium (VLISM) will likely come first: https://link.springer.com/article/10.1007/s11214-022-00943-x