There was a pretty awesome "space age" of video games from the mid 80s to mid to late 90s, and what I've always loved about some of those games is that sense of isolation and adventure, a more of a Star Trek approach with emphasis on exploration, resource gathering, trading, communicating with unknown alien races, diplomacy and a usually (and unfortunately) undercooked combat.
I like Elite: Dangerous and have spent dozens of hours on it, but IMO it lacks that sense of lonely galactic adventure, I think mainly because of the way it handles instanced interplanetary flight (it really doesn't click with me for some reason) and the setting and its goals (big industrial hulks in space, dry-feeling empires and democracies, political battles between factions etc.). It has a lot of freedom, but the confines within which you are set free don't really click that much with me.
No Man's Sky sounds like something I'd really be into, with maybe a bit more contacts with alien NPCs, diplomacy etc. but I generally like the direction they're going for.
If you're into trying some older games OP (as in PC DOS), you might like stuff like the Starflight/Protostar games, Star Control, Captain Blood, Millennia: Altered Destinies, Ironseed, basically space trading and exploration or 4X games but revolving around a single person or a small crew set in a grand space opera, instead of building an empire or being a privateer in a political conflict.
EDIT:
Also, even though it's not a game yet, try Space Engine and just fly into a black hole while listening to Interstellar's OST.