I'm curious about what happens when a soloist walks off stage after a performance. Where do they go? Where does the conductor go? Everything backstage is a mystery for me.
In between pieces, a soloist and conductor will walk off stage and just stand in the wings briefly. It's a chance to pause, switch gears before the next piece, maybe have a drink of water. It allows time for any changes that need to happen on the stage, such as certain musicians leaving or entering, depending on who is needed for the next piece.
After a concert is over, if the venue provides dressing rooms for the soloist and conductor, they'll go there, rest, maybe change clothes, maybe greet guests. Again, it's a chance to switch gears, especially if they'll be going out to a reception afterwards.
First they go to their dressing room, pack their instrument away, get changed, possibly shower. If there's catering, they might stay at the venue for a while. If they're well known they might have to sign a few autographs or talk to well-wishers at the stage door. Then they'll do what anyone else does when they've finished work: go home (or to their hotel) or go out (to eat, drink, party...). Often the soloist and the conductor and their partners will go out to dinner.