Proxima Centauri is only a handful of lightyears away, and it has planets in inhabitable zones.

Doesn't mean there is life there, but it's promising. A space probe sent there, once it arrives, could still fathomably send signals back to earth that could be conceivably used by human researchers.

Of course, if fusion-based acceleration becomes feasible in the next few decades, it would arrive long before any probe we try sending now. So there's the trade-off...