Some of the original highway between Moto-Hakone and Hakone-Yumoto, remains today, with the best-preserved section running from Moto-Hakone to Hatajuku via the Amazake Chaya, a tea house serving amazake (hot, sweet rice wine) and Japanese snacks.
It's a two-hour walk, just under half way to Hakone-Yumoto, but from there the modern road runs over the old highway, and there's no footpath for pedestrians.
There are half-hourly buses along the route, so it seems you can still walk the good bit of the ancient highway and use the bus to get you the rest of the way.
The traveller's most likely way into Hakone is through Odawara and Hakone-Yumoto.
Personal experience (weather conditions permitting) suggests an anti-clockwise progress through the area. Odawara, on the main Tōkaidō Shinkansen line, is an obvious starting point, though the private Odakyu railway offers services from Tokyo's Shinjuku station all the way to Hakone-Yumoto, including the Romancecar limited express.
From Odawara, the Hakone Tozan Line runs along the Hayakawa River valley on the way to Gora, with switchbacks as it makes its way up the steepest gradient on a Japanese railway line.
From Gora, the Hakone Tozan Cable Car goes up the mountainside to Sounzan, at one end of the Hakone Ropeway, which carries visitors on a thirty minute two leg journey to Tōgendai, on the shore of Lake Ashinoko.
With ropeway cars departing at one-minute intervals, given the right weather conditions, visitors can enjoy views of Mount Fuji as they cross the Ōwakudani geysers in the Great Boiling Valley.