Decide what the trip is supposed to deliver
Hakone and Fuji from Tokyo are often treated as one idea, but they are really three: Hakone for transport loops and onsen, Kawaguchiko for more direct Fuji viewing, and an overnight stay for calm and weather margin.
Choose Hakone if you want the area, not just the mountain
Hakone is strongest when you want a combination of scenic transport, ropeway, Lake Ashi, museums and hot-spring atmosphere. It works as a day trip only if you accept that you are doing one clean version of Hakone, not trying to add everything.
Choose Kawaguchiko if Fuji is the real priority
Lake Kawaguchi is one of the easiest Fuji areas to access from Tokyo. If your real goal is a strong Fuji-facing day, Kawaguchiko is usually the cleaner choice.
When an overnight stay is worth it
Stay overnight if you want onsen, early or late hours in the area, a second weather chance or a calmer rhythm.
When to get personal help
Personal planning is worth it if you are torn between Hakone and Kawaguchiko, if you want to add an overnight stay without weakening the whole route, or if Fuji views are a major trip goal.