if you do hakone on the first day, you can deposit your luggage at your accommodation before heading off to do the round course, which would take just a few hours, and you have the rest of the day to enjoy your hotel/ryokan stay (assuming you set off from shinjuku early in the morning). you wouldn't have the luxury to do either if you went direct to fujikyu highland from shinjuku.
so, i would do shinjuku-hakone-fujikyu highland-hakone-shinjuku(?) if i were you.