Kharkiv was as important as Kyiv. It's the second largest city in Ukraine, old capital city and close to the border with Russia. If they couldn't take Kyiv they would take Kharkiv. Kherson is not that important from strategic point of view when compared to the two biggest cities.Kharkiv has never been that important to Russia anyway. The main focus has always been Kherson. Kherson is vital to Crimea's water supply via the Dnipr. In fact, it can be said the rationale for starting the war in the first place is water.