You may recognize the fishhook curve of bright stars that is Scorpio's tail. It is near the tip of the tail, as I recall.
Scorpio borders on Sagittarius (not as easy to identify) and official sky maps show the galactic center in Sagittarius territory. But it is very close to the tip of that "question mark looking" hook-like curve of scorpion stars.
One quarter of a Galactic Year is what? something like 50 or 60 million years. So solar system will be some 90 degrees around in its orbit and Center will be totally NOT in the plane of the ecliptic.
It will be at around 60 degrees south ecliptic latitude. If you picture the ecliptic south pole? the "down" direction if you visualize planet orbits counterclockwise in a level plane?. then Center will be more close to south ecliptic pole.
Very roughly it will be not so far from the Earth south pole direction. It will be a southern hemisphere feature, not like today.
The plane of the ecliptic, essentially the plane of the solar system, is TILTED BY 60 DEGREES compared with Galactic plane.
Of course both Scorpio and Sagittarius are on the ecliptic (they are "zodiac" constellations).
I guess if you want to view that part of the sky where the Center is, it would be rising at midnight around 1 April.
And two hours earlier (10PM) around 1 May. I'm thinking northern hemisphere, e.g. US latitudes. You would go outdoors say four hours before midnight around 1 June and look just about due Southeast and Scorpio would be rising. Head first as I recall. So a bit later the tail would be completely up over the trees and you could basically point your finger at galactic Center. If you were out away from city lights and it was a dark night you could see the Milkyway all along the Horizon both the east and west of you. The plane of the Galaxy would more or less coincide with your ground plane that you are standing on. (Say if you are around 30 degrees north latitude).
Thats how things are oriented when the Center rises (to the SE) say around 10PM around 1 May. Glad you asked. It reminds me of some nice time in years past.