Did Claudia and Jamie ever go home?

Yes, Claudia and Jamie eventually went home at the end of the story "From the Mixed-Up Files of Mrs. Basil E. Frankweiler" by E.L. Konigsburg. After their adventure of living in the Metropolitan Museum of Art, they returned home with a newfound appreciation for their family and life. Their experiences profoundly changed them, leading to a deeper understanding of themselves and their relationships.