The main road from Gotemba to Hakone is the route 401 which turns into the route 138 a bit onto the mountain. The route 401 actually splits off and later turns into the maginifcent Ashinoko Skyline. Anytime that you are thinking about driving the Ashinoko Skyline, it is worth driving the route 401 as well, especially the upper part.
While the Ashinoko Skyline is more a scenic route, the route 401 is more a drivers route with a lot of tight corners and few stopping points. There is one viewpoint in the middle, at a small resthouse, which provides a good view over Gotemba. Also at the bottom there is a parking with toilet which gives a great view on Mount Fuji.
Although the road condition is not the best at the bottom half of the route, once you reach above the treeline on the upper half of the course there is very good road quality. This route is toll free at the time of writing.
Google Maps location link:
Route 401 entrance