If you want lots of gold, go to the source: neutron star mergers.
Neutron star binaries that are about to merge can be located by their gravitational waves. Use triangulation from widely separated detectors. The gravitational wave signal will also tell you how soon they will merge, so whether your collector will get there in time. Obviously, having FTL travel helps in getting there (and back) but is not strictly necessary.
Tradeoff: be close to the kilonova to collect lots gold without needing a huge collector. Be far from the kilonova to avoid being destroyed by the explosion. Given a guess of how much matter gets ejected in the explosion, it would be easy to calculate kilograms per steradian, for collector design. The most ambitious would be to completely surround the explosion and achieve 100% yield.
Along with the gold, you will collect a lot of other heavy elements, including a lot of highly radioactive stuff, so you will have to refine. Probably lots of superheavy elements: what superheavy elements can you get from a kilonova but not from a supernova?
The matter probably gets ejected at relativistic speeds, so radioactive ejecta even with very short half lives will survive out to a very long distance. This is good for science -- experiment on superheavy elements with short half lives -- but annoying for mining and refining.
Previously on mining neutron stars for fun and profit: (1) and (2).
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