"Посольство" is in the accusative case, and "посольстві" is in the locative case, right? Why wouldn't we use the locative case here?
Truly speaking, I think "Ти ходила до посольства" sounds better in Ukrainian than "Ти ходила у посольство".
But anyway, after "у/в" + destination we do use the Accusative case, with "до" + destination we use the Genitive.
The Locative is used with "у/в" + place you're staying in (as opposed to destination). So you'd say "Я у посольстві", meaning "I'm at the Embassy".