In the south, to secure a warm water port and restore crimea's fresh water supply. Elsewhere, because they're trying to force Ukraine to come to the bargaining table (or surrender, but that still seems unlikely). They could withdraw all their troops from the rest of the country once the war is over in return for Ukraine signing a neutrality agreement.
Edit: I should add that this is a guess, but I think these are Putins main goals.
In the south, to secure a warm water port and restore crimea's fresh water supply. Elsewhere, because they're trying to force Ukraine to come to the bargaining table (or surrender, but that still seems unlikely). They could withdraw all their troops from the rest of the country once the war is over in return for Ukraine signing a neutrality agreement.
Edit: I should add that this is a guess, but I think these are Putins main goals.