Is expiation for breaking an oath (kaffarat yamin) obligatory for someone who swore, saying: "By God – God willing – I will not go to a certain place," then went there, and what is its measure?

The phrase "bi-idhnillah (by Allah's will)" is an exception to an oath. For the conditions of the exception to be valid—so that no expiation is required when going to the intended place—those conditions must be met. If the conditions for the exception are not met, then an expiation for the oath becomes obligatory. It is permissible to give the expiation before breaking the oath.