During the first part of a war the major target should ultimately be troops, not land. Once troops are out of the way land is just a matter of resources and luck. Splitting your stack is effective during the land phase to more quickly conquer land but if the enemy has a large stack somewhere you are generally better off first taking out that stack with overwhelming force (i.e., 1 stack with everything you can spare). Even better if you can get another AI to help take down that stack of troops.
If you are going to strategically strike inside enemy territory (such that if you do take the city you would be surrounded by culture) then either raze that city use it to draw the enemy stack to you. You may also want to consider, after making peace or getting capitulation, liberating that city for the positive diplo. Many of the buildings will have been demolished just from capturing and, as I just said, you will have reduced the power of the AI. You should also consider pillaging in this situation.
Normally, I find myself wanting land so I try to form a coherent and defensible border with the cities that I take. Alternately, I'll work toward the capital and other strong points without razing but eventually my goal is capitulation so I ultimately want to return the cities in good order so my new friend will actually be of some help and won't require overly much assistance in defending their land.