New Year Cheap Hotel in Tokyo and Hakone

I will be in Tokyo from 29 Dec-3Jan, I am now struggling with the lodging problem as I noticed most of the hotel in Tokyo city are fully booked and the remaining are expensive(more than 200 USD),can anyone advise me what should i do? I am going with my husband and capsule hotel is definitely not my choice.I am having the same problem in Hakone, how can i get a budget onsen hotel on 30 and 31Dec? I am really worry.....

I am now struggling with the lodging problem as I noticed most of the hotel in Tokyo city are fully booked and the remaining are expensive(more than 200 USD),can anyone advise me what should i do?

Use a better hotel reservation website! The Japanese version of Rakuten Travel, for example, comes up with 429 hotels in Tokyo, which still have vacant rooms for the New Year holidays, many of them cheap. The English version lists not quite as many, but also offers a wide range of hotels at various budget levels:
http://travel.rakuten.co.jp/en/

Finding something in Hakone, however, will be more difficult. You might want to visit it in a day trip from Tokyo.

Thanks a lot Uji, I am considering your suggestion to take 1 day trip to Hakone, any cheap package that you can recommend? Or is it convenient to go by ourself during new year time(around 31 - 2 Jan)? Any recommendation nearest onsen trip or snow trip from Tokyo? Appreciate your input.