There's one thing I haven't done yet in NMS, a very big thing, gone to the center and a new galaxy. I just can't get myself to leave the current one. It's just too nice.
At the end of the Artemis missions you get to choose a new galaxy, I picked Lush like most people do.
When you place a random base computer you can leave your new galaxy and always return, that's what I did.
From any station you can teleport back and forth.
When you decide to open up another galaxy be sure you're using your crappiest ship and multitool since a lot of modules will be damaged when you get there.
By any means don't fly a Living Ship when opening a new galaxy, those things are an enormous pain to repair.
Maybe you already knew all this stuff but it never hurts to share some tips.