I am planning to go to Hongkong this december and I will be staying for 1 week there with my family. What is the best hotel or accomodation in price and and in service.

YMCA is not bad, but Metropark in Mongkok (the one near Kowloon Tong) is a great place and they have great deals, it is a business-style hotel with excellent service and a pool and gym on the top floor deck. I spent a week there last August with my two daughters and the rate was under $700HK per night. If you want to stay out of town, a nice place to relax near the beach is the Silvermine Beach Hotel, it is an easy ferry ride from Hong Kong Island. Some rooms have been renovated and face the ocean. Great for families with young kids. You can spend the day at the beach or go to town very easily.

I would be moving to Yokohama, Japan for 2-3 months and am looking for an accommodation for that time period. Does Japan has a Paying Guest system in place? Are the accomodation fully furnished? I am single so open to share accomodation

Getting private accommodation for a foreigner is very difficult process. Short term fully furnished places are very expensive. I would expect somewhere in the 1000-2000 USD a month rent, for short term private accommodation, fully furnished places. If you were there for a year or more, then of course more affordable unfurnished places, but usually you need a Japanese guarantor, and 2 year contract.

Fort short term like 2-3 months you should look into getting youth hostels and guest houses. Much cheaper and affordable rent, of course you share the place with other people, sorta like a dorm. But usually you get a private room, but things like the common area, kitchen etc are shared. But its certainly more affordable for short term.