Hi, we are intending to explore the countryside of Tokyo for about 10 days. We have 5 days in Tokyo itself. Would anyone help comment on below itinerary and provide ideas for another 5 days before returning to Tokyo? Thanks!

Day 1
Pickup car & drive out of Tokyo to Hakone (is 3 hours sufficient to cover the jam if I drive out from 9am?)
Open-air Museum
[Please recommend an inexpensive and clean or new hakone hotel for 2N- any reviews on Villa Hakone Stage?]

Day 2
Cable Car and Ropeway to Owakudani (great boiling valley) try black eggs + GeoMuseum
Take ropeway down to Togendai to take pirate ship cruise across Lake Aishi to Hakonemachi-ko
Lunch at Tatsumi, 69 Hakone, Ashigarashimo District, Kanagawa 250-0521, Japan
Walk to Hakone Checkpoint
Amazake-chaya Tea House?
Hakone Shrine?
[Staying at Villa Hakone Stage may help solve the [url=https://www.tripadvisor.com.sg/RentalCars-g298184-Tokyo_Tokyo_Prefecture_Kanto.html]car issue. Otherwise if I stay at another hakone hotel, I do not know how to collect the car from Gora station at the end of the day?

Day 3
Check out & drive to Mount Fuji
Fuji Safari Park
[Japan should be quite safe without any [url=https://www.tripadvisor.com.sg/RentalCars-g298184-Tokyo_Tokyo_Prefecture_Kanto.html]car breaking incident if I drive straight to Fuji Safari without dropping the luggage at the fuji hotel?]
[Please recommend an inexpensive and clean or new fuji hotel?]

Day 4
Fuji Q highlands

Day 5
Narusawa Ice Cave
Fugaku Wind Cave
Aokigahara Forest
Saiko Iyashi-no-Sato Nenba (Traditional Japanese Village)

Day 6
Momiji Tunnel [not sure if I should go arakurayama first or Momiji tunnel in the morning or evening?]
Kawaguchiko Music Forest Museum
Arakurayama Sengen Park

Your links go to some tripadvisor page and I don't understand why you linked them.

>> Staying at Villa Hakone Stage may help solve the car issue. Otherwise if I stay at another hakone hotel, I do not know how to collect the car from Gora station at the end of the day?

I don't understand how your Day 2 works if you stay at Villa Hakone Stage the night before. That lodging is near Togendai. You can start at Togendai with the boat across the lake to Moto Hakone and make one of two loops:1) by buses to Gora via Kowakien/Yunessun or 2) bus to Hakone Yumoto and Tozan railway to Gora. From Gora then the cable car and ropeway to Togendai.

Your Day 2 has you driving to Gora (I think) ending in Moto Hakone or Hakone-machi. If your car is in Gora then you could take either of those two routes by bus to get back to it. Or reverse the route: boat, ropeway, cable car. Maybe taxi.

Take a look at the transit map here: Hakone Free Pass (Hakone Freepass) (japan-guide.com)

See if you can get a rental car in Hakone Yumoto or Gora. I would expect there would be rental cars in Odawara. You could get a Hakone Free Pass and take the Odakyu train (Romance Car is best) to Odawara or Hakone Yumoto. Stay in one of those places and use the pass to get around. You don't need the car until Day 3.

More info here: Hakone Freepass - Odakyu Railway: Connecting Shinjuku, Hakone and Enoshima

The last four days look good. By "fuji hotel" you mean somewere in Fujigoko area, like Kawaguchiko, I think. Most if not all of your stops are shown on the map on this webpage: Lake Kawaguchiko - Fuji Five Lakes Travel (japan-guide.com)

I would not have a concern with leaving luggage in a car in Japan, assuming it is in a trunk/boot. I have not done that, though. Seeing how most of the tourists to the safari park, especially people using the parking lot, are going to be Japanese, your luggage would probably be ok if you left it on the roof of the car. If anybody would break into your car, it would probably be a foreigner, but foreigners would probably be gettng to that place on a tour bus, so not likely criminals. It's not Hawaii.

Am joking about leaving stuff on the roof of the car: It will probably get rained on..

Thanks all. I have no idea why the links appear too but I can't seem to change my post now.

I will probably get the 2 or 3 days Hakone Pass and then get the car from Day 3 or 4 onwards.

Forgot to add: the answer is yes, you want to take the ropeway in Kawaguchiko.

You can find a nice ryokan near Hakone Yumoto station. It would be convenient for the train from Shinjuku and it is on the Hakone Loop. So, you could drop your stuff there and go to that spot you mentioned on the first day.

The drive described in the link below would be less than a 3-hour drive from Kawaguchiko (to Ueda or Karuizawa). One of the stops, Kusatsu Onsen, is wonderful. The route goes over to Nikko and then Utsunomiya (gyoza!). Not far from there to Tokyo.

Japan Romantic Road (japan-guide.com)

Have not driven in Japan for a long time but driving in and out of Tokyo is a real pain. Also driving to and around Hakone on the weekend is quite crowded so I would do that portion of the trip during the week.