Nagoya to Tokyo - Hakone day trip?

We will be traveling from Nagoya to Tokyo and would like to stop and see Mt. Fuji on the way there. Would Hakone be a reasonable place to spend most of the day, or would it be way too overwhelming for a day trip? We don't care about seeing everything or completing the loop, as I understand Hakone is at least 2-3 days for most travelers. We are also looking at Kawaguchiko but are open to any and all suggestions. Thanks!