2 days 1 night at Gotemba & Mt Fuji

Hi, I'm looking for a ryokan/hotel to spend 2 days 1 night at Gotemba & Mt Fuji area, in early August.

We are intending to make a visit to Mt Fuji , and then spend a day shopping in Gotemba outlet.

Which area should I find a ryokan/hotel to stay 1 night in, to fit in these 2 places? Gotemba or Hakone? The budget for the ryokan / hotel is around USD 300.00, is it feasible?

Need advice from someone as soon as possible!

I recommend to overnight in a ryokan in Hakone. There are dozens to select from:
http://www.japanican.com/
http://travel.rakuten.co.jp/en/

Thanks Uji-san, will go take a look at these websites.

If we are to stay at Hakone for 1 night, how would you recommend the itinerary to be?

E.g From Tokyo, go to Mt Fuji, and then check in at Hakone hotel/ryokan at night. Next day check-out & go to Gotemba outlet?

And do we take bus/trains around?

If we are to stay at Hakone for 1 night, how would you recommend the itinerary to be?

Do the round course in Hakone:
http://www.japan-guide.com/e/e5210.html

If you want to go closer to Mount Fuji, then you should consider visiting the Fuji Five Lake region instead of Hakone. But seeing both plus Gotemba would be too packed:
http://www.japan-guide.com/e/e6900.html

So, I recommend either Fuji Five Lakes or Hakone. Personally I prefer Hakone, but if views of Mount Fuji are very important to you, it might be better to select the Fuji Five Lakes due to a higher probability of being able to see the mountain from there.

And do we take bus/trains around?

It is explained on the following pages:
http://www.japan-guide.com/e/e5206.html
http://www.japan-guide.com/e/e6905.html
http://www.japan-guide.com/e/e5213.html