NASA has discovered Kepler-168f, a beautiful, earth sized planet 500 light years away. It is 40% larger than Earth, it has a 50% smaller sun. Another option would be the inhabitable super-earth 13 light years away, orbiting the Kapteyn's Star, a beautiful red fireball of awesome. Both have optimal life supporting climate and conditions.
What I'm proposing is we introduce this into destiny, sooner rather than later. There are many different story line options as to how this could play out. We could find one of these planets, previously untouched, but colonies under attack by an unknown threat. We could colonize one of the planets ourselves, build our own personal towns, each guardian, and defend them as a new game mode option, like clash of clans or something like that. Or we could rescue one of the planets from the darkness in a brand new raid. However we introduce one of these beautiful planets, I vote we visit them, save them, or conquer them one way or another.
Edit: The "Hell yeah, get me some of that" option is saying that we rush straight to the other Galaxy. Wether it be some amazing opportunity that calls us there, or some terrifying threat we need to stomp out at the root, that is what this option is for.
On the other hand, the "Why not both" option means we fight our way out, stabilizing our Galaxy, or at least a solid path out of the Galaxy, in order to reach this new space.
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There are more than enough possible locations in our own solar system to explore before we start thinking about others. It also makes sense from a story perspective to stay here. We still haven't completely taken our own system back, and the only Guardians with any real reason to go to another system would be Dead Orbit-aligned Guardians. Since that's kind of their entire end goal. As a side note, I'm not sure where you got your information about this system, but according to the actual astronomy journals, you are completely wrong about it. For one, it's a lot farther away than 13 ly, closer to 1400. And the star isn't red, being a spectral-type G2V main sequence star, like the Sun.