Getting ready to go out on my first long distance exploration trip and have a question about black holes. Do black holes show up on the system map? How do you find them? Thanks
The easiest way is to set the filter for the galaxy map to only show non-sequence stars, which will show neutron stars and black holes only. In terms of finding some rapidly, head about 1,000LY down or up from the galactic plane (I usually go low) and fly in towards the core. If you keep checking the galaxy map using the filters as above, you'll run into non-sequence stars fairly frequently and often will find a relatively dense 'layer' of them. There's no way to differentiate between neutron stars and black holes once you've filtered the map other than mousing over the star and seeing what it is.
Also bear in mind that you will often have to get close to a black hole before you'll see the gravitational lensing effects, they aren't all huge.
As for the system map, as stated above yeah they do show up but it's as a black circle so after you do an advanced discovery scan on the system, look for orbit markers that don't seem to have a planet or star, mouse over the space and you should find your black hole. Obviously if you jump to a system that's shown as a black hole on the galaxy map the black hole will be the main star so you will jump to it. To avoid soiling your flightsuit, especially if it happens to be in a binary pair with a neutron star or white dwarf, get into the habit of zeroing your throttle during the jump transition so that you arrive at a dead stop.
Last tip - especially if you're using the neutron star jump boosting, be very careful when you're filtering the map that you don't fly into a region with no scoopable stars and run out of juice. I usually filter for two start types, non-sequence and one of the common types such as M or A. It's still easy to spot the non-sequence stars because you only have two colours of system on the map, grey (non-sequence) and either red (M) or blue (A) but you'll always know you have scoopable stars around you to refuel. If you notice that the scoopables are thinning out, just start to make sure that your last long jump before being out of fuel is to a scoopable with a nearby boostable star - that way you can fuel up at the scoopable, spend a minimal amount of fuel reaching your next jump boost system and get back to rapid travel.