I am a train geek so I am biased and will recommend taking Odakyu Line’s Romacecar to Hakone.
There are few different type of trains for Romancecar.
Romacecar Trains
VSE (Vault Super Express) 50000 and LSE (Luxury Super Express) 7000 Romancecar has front seating where you get to experience front view of the train. Price of those front seats are same as rest of seats but front seats are prime seats, if you got a ticket for those front seats then you sure are lucky! I will definitely say you should take Romacecar, not Shinkansen. Current schedule for VSE and LSE Romacecar departing Shinjuku are:
Weekdays (Monday – Friday)
10:00 a.m. departure Hakone no. 13 (VSE)
10:40 a.m. departure Hakone no. 15 (VSE, subject to change)
11:40 a.m. departure Hakone no. 19 (LSE, subject to change)
1:40 p.m. departure Hakone no. 29 (VSE)
2:10 p.m. departure Hakone no. 31 (VSE, subject to change)
5:10 p.m. departure Hakone no. 43 (VSE)
5:35 p.m. departure Hakone no. 45 (VSE, subject to change)
Weekends (Saturday, Sunday, and Holidays)
7:00 a.m. departure Hakone no. 1 (LSE, subject to change)
8:30 a.m. departure Hakone no. 7 (LSE, subject to change)
9:00 a.m. departure Hakone no. 9 (VSE)
10:10 a.m. departure Hakone no. 13 (VSE, subject to change)
10:40 a.m. departure Hakone no. 15 (LSE, subject to change)
12:10 a.m. departure Hakone no. 23 (LSE, subject to change)
12:40 a.m. departure Hakone no. 25 (VSE, subject to change)
1:40 p.m. departure Hakone no. 29 (VSE, subject to change)
2:10 p.m. departure Hakone no. 31 (LSE, subject to change)
3:40 p.m. departure Hakone no. 37 (LSE, subject to change)
4:10 p.m. departure Hakone no. 39 (VSE)
5:10 p.m. departure Hakone no. 43 (VSE, subject to change)
5:40 p.m. departure Hakone no. 45 (LSE, subject to change)
LSE trains has regular wagon service with snacks and drinks. VSE trains has a café which has seat service, where attendants will serve drinks at your seats where drinks are served using real glassware.
Food and drink service on Romancecar
Food and drink menu on Romancecar
As for the front view from Romancecar, following is YouTube video of Romancecar front view from Shinjuku to Hakoneyumoto.
YouTube Video Romancecar
Yes, the video is an hour and 30 minutes long. But if you jump to 1:05:00 (one hour and five minutes mark) on the video, after going under Toumei Expressway on clear day there will be a view of Mt. Fuji in right front of you. It will be a nice ride to Hakone.
