Hakone by private bus

We're planning to visit Hakone on a day trip during April 2011 (5 adults 5 children).
W'd like to see beautiful views of the lake Ashi as well as Mt. Fuji. We would also like to cruise the lake in the Pirate ship and go on the Ropeway. Anything else on the way is also ok.
We'd like to end the day shopping at Gotemba Outlet for 2 hours and hope to reach Shinjuku by 8pm.
Where would you suggest we start and where can we have lunch?
We don't want to hike as there are many children with us and we also have the mini bus.
Thank you.
JnG RnT

Owakudani rope way station has a view restaurant on top. You can see Mt. Fuji(in a clear day) while dining.
Hakone-Machi port has also a fast & cheap noodle shop as you disembark the ship and a restaurant in the main building.
There are some snack shops but other than these places you need to find on your own on the main road.
Go to the hill top Onshi Park between Hakone-Machi port & Moto Hakone for the view of the lake & Mt. Fuji.

I'm assuming that by private or mini bus that you mean a rental vehicle. If that is the case, then I would suggest the following route from Shinjuku.

http://maps.google.com/maps?q=shinjuku,+tokyo,+japan+to+owakudani+Stat...

(if the link doesn't work, either cut and paste it into your search engine or go to Google.com and type "shinjuku, tokyo, japan to owakudani Station, Hakone, Kanagawa, Japan" into the search bar. When you get to the Google Maps site, click on the car icon on the left side and it will present two routes: one with tolls and one without. The one without tolls is actually less time consuming. (Hint: I would allow more time than what Google maps quotes.)

Owakudani Station is a stopover on the ropeway as mentioned by the previous poster. It is one of the few places that appear to have parking. Take the ropeway down to Togendai and board the pirate ship there.

After touring Lake Ashi and Hakonemachi, return to Owakudani Station and drive back the route that you came to Gotenba and the outlet mall.

Have fun and drive carefully!

Thank you both'amazinga' and 'geogeek1'. Additional questions: we're hiring a private bus with a driver. Can he drop us off at Gora where we can do some activities at the Crafthouse. Then cable car to Sounzan and ropeway stopping at Owakudani for lunch. Then Togendai and straight to Moto-Hakone, visit Hakone Shrine and board the private bus at 3pm to Gotemba. If we start at 9am at Gora, will the timing be ok? Would it be better vice versa?

...yes, it can be done with plenty of time.

When we were there, we arrived at Gora at 11:00 AM, had lunch there, arrived at Hakonemachi at 1:40 PM (by inclined railway, ropeway, and pirate ship), walked to Motohakone and arrived at the bus stop there by 3:00 PM. We were doing all this at a leisurely pace.

...if you start in Motohakone, you will end up much closer to Gotenba. That would probably be the better route.

As recommended by geogeek1, if we start at Motohakone, visit Hakone Shrine, Pirate ship to Togendai, ropeway to Owakudani and lunch there (is it expensive?). Then ropeway to Gora, Gora Park's Crafthouse. Board our private bus at Gora 3-4pm,to Gotemba. Would purchasing Hakone Free pass still be worth it (6 adults 6 chidren) and can we obtain them at Moto-Hakone?
If we arrive at Moto-Hakone at 10:30 am do you think we can add other places in before Gotemba?
Thank you in advance.