Equal join the two tables on City and update [City FK] with Table1.ID. I don't think you have to specify criteria (WHERE City in one table = City in the other) due to the equal join. Then you can go into table design and delete the City field. The thing is, what is the purpose of first table? If it's customers, the city fk should be there, not the city. If it's a city table, the customer fk should not be there. Wondering if you should research database normalization before going any farther.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.