Although the answers are gievn by above poster, I'd like to confirm again.
>>I am a bit confused. The pricing that you gave are all for 1-way travel if I do not buy the Freepass that originate at Odawara?<<
Yes, the prices on my routing 1) and 2) are all for one way.
>>If I buy the freepass that originate at Odawara, it would cost 3900yen. From Odawara to Hakone-Yumoto, another 300yen. Then from Hakone-Yumoto to Gotemba, take the Odakyu Hakone Highway bus (which comes free with the Freepass). From Gotemba, take the free Odakyu Hakone Highway bus back to Hakone-Yumoto then pay another 300yen to go to Odawara to catch romancecar back to Shinjuku.<<
The Odawara - Hakone-Yumoto segment on Hakone Tozan Line is fully coovered by the pass.
>>There are 2 ways to get from Gotemba to Shinjuku:
(1) Free Odakyu Hakone Highway bus – Odawara – Shinjuku (as stated above)<<
IMHO, this routing doesn't make sense at all. It takes about two hours from Gotemba to Hakone-Yumoto, then another one hour and a half to Shinjuku. Way too long duration.
>>(2) Gotemba, pay ??yen to catch the JR to Odawara – Shinjuku<<
You might take the JR Gotemba Line train from Gotemba to Kozu, then change to JR Tokaido Line to Tokyo, then travel onto Ueno by Yamanote or Keihin-Tohoku Lines. It's 1,890 yen in total.
Backtracking to Odawara doesn't make any sense.
>>Can I catch JR from Gotemba to Shin-Matsuda and then use the Freepass to link back to Shinjuku? Or must the freepass start at Odawara only?<<
If you go this way, you might want to buy the Hakone Free Pass from Shinjuku (2-day one for 5,000 yen). The Shin-Matsuda - Shinjuku segment is fully covered by the pass.
However, you need to pay additional 480 yen for the JR ride from Gotemba to Matsuda.
Suppose you leave Gotemba at 4 pm, I'd make a comparison of the price and specific connections.
1) JR Gotemba and Odakyu Lines via Matsuda:
Gotemba 16:12--(JR Gotemba Line local)-->16:43 Matsuda--walk-->Shin-Matsuda 16:56--(Odakyu rapid express)-->18:11 Shinjuku
Total cost: 480 yen (JR portion only) / Use the Hakone pass originating in Shinjuku as stated above.
Please be warned that JR Gotemba Line runs mostly once an hour, and the Odakyu Line rapid express and express trains are always busy. No guarantee of getting a seat from Shin-Matsuda.
2) JR Gotemba and Tokaido Lines:
Gotemba 16:12--(JR Gotemba Line local)-->16:59 Kozu 17:07--(JR Tokaido Line local)-->18:19 Shimbashi 18:23--Yamanote-->18:31 Ueno
Total cost: 1,890 yen
3) Odakyu Hakone Highway Bus:
Gotemba 16:05-->17:45 Shinjuku
Total cost: 1,630 yen
Apparently this is the best mode of transport on this segment in terms of frequency (every 30 minutes), comfort. But it's you that decides which mode of transport to take.
4) JR-Odakyu direct limited express 'Asagiri'
Gotemba 17:55--Asagiri8-->19:36 Shinjuku
Total cost: 1,970 yen (JR portion 480 yen and limited express surcharge 1,490 yen) / Use the Hakone pass originating in Shinjuku to be exempted from paying for the Odakyu segment.
All the JR schedules are valid from 15th March.
From Shinjuku to Ueno, take the Yamanote Line train, 190 yen, 24 minutes.
>>Can I clarify that taking the RomanceCar from Odawara to Hakone-Yumoto is free and covered by the Freepass? The Hakonenavi website states that to use the Romancecar between Odawara Station and Hakone-Yumoto Station, passengers must pay 200 yen for a reserved seat ticket, in addition to their ticket or Hakone Freepass.<<
It's fully covered by the total price of the Shinjuku - Odawara segment.
>>Actually, since I am staying in Ueno, does it make more sense for me to start from Ueno to Odawara or Ueno-Shinjuku-Odawara? Is the difference in that from Shinjuku, it’s the romancecar hence faster traveling and also reserved seats?<<
Ueno to Odawara via Tokyo by JR: 1,450 yen, 1.5 hours, every 10 minutes frequency on Tokaido Line.
Ueno to Odawara via Shinjuku by JR and Odakyu: 1,910 yen (Romance car), 1 hour 50 minutes, twice hourly frequency (Romance car). 870 yen less if you take the express.
>>Can I also know where does the Tozan bus stop in Gotemba? How do I get to the premium outlets from there?<<
There are bus services from Gora Station to the outlet, 70 minutes duration. Not sure they are covered by the pass.
Weekday: 8:40, 9:40 and several afternoon services
Weekends and holidays: 9:10, 10:35 and several afternoon services
If the services doesn't meet your schedule, catch the Odakyu Hakone Highway bus to Gotemba, and change to the complimentary shuttle to the outlet. It runs every 20 minutes.
Hakone Free Pass info