Anything worth visiting under 500Ly has probably been cherry picked already. Every 100ly passed that towards the core increases your chances exponentially because the density of the stars get higher.
And so should the thermal, radiation, and gravity limits be going up exponentially. That is something I think Frontier got wrong. The Core is Death Incarnate, once you get close enough. Melt, get microwaved/nuked, or be torn to bits in a misjump.