What is the difference between 明日何をしますか and 明日どうしますか？
I have come across the following question and answer:
So, I wonder if I can say 明日何をしますか instead.
Given the context:
a man was borrowing an umbrella at a station, and was asking a station worker how and when he could return it.
どうしますか is absolutely better than 何をしますか, because in this situation, they respectively mean:
明日何をしますか What am I going to do tomorrow?
明日どうしますか What am I going to do with it tomorrow?
Incidentally, this is not the most natural phrase native speakers would utter in this context, but presumably they want to reduce grammar repertoire for beginner students. For example I would say:
明日どう（すれば／したら）いいですか What should I do (with it) tomorrow?
In the bigger picture, it is but a tip of an iceberg, a total discrepancy in work division of question words between Japanese and English. To put abstractly, English selects question words grammatically (i.e. in relation to the original sentence) while Japanese semantically. It is very much complicated, but taking your example, both the speaker and the hearer are supposed to recognize a common matter about a borrowed umbrella. Thus a next whatever step you take is an instrument to solve, or in any way to deal with this final goal. This sort of action is always governed by どう in Japanese, otherwise it will sound that you suddenly throw in a new, independent topic.