My father-in-law was a Yung Kee habitue for many years until he passed away. However, his favorite public restaurant was Fook Lam Mun on Johnston Road in Wanchai, quite close to your Hotel. One thing about it is that depending on your status and how well known you are to the staff, you are directed to different floors. Where we ate, there was a wall of wine bottles (typically the best Bordeaux and other great wines which were being kept by regular customers for their visits to the restaurant.) There was a separate section for partially opened Cognac bottles owned by customers also. We never ate at the highest floor of the restaurant. I don't think the food is any different on the different floors. I saw my first Maybach there - a customer and his entourage coming in for a meal.
You can check the Michelin Guide. There are many starred restaurants in HK, including Fook Lam Moon and both the fancy Chinese and French restaurants at the Four Seasons. However, I ate lunch at a one star dim sum restaurant (on Canton Road in Kowloon, across the street from Ocean Terminal, near the Star Ferry) which specializes in steamed dumplings (Shao Lung Bao). Lunch was less than HK$100, or US$12, probably the cheapest 1 star Michelin restaurant meal in the world.
Some of the best food in Hong Kong is not accessible to visitors without some contacts. They include a fair number of private clubs who only serve their members and guests and a large number of private residences where meals are prepared and served for a table (typically 8 people) of guests. The latter are unlicensed and do not advertise, so it is word of mouth. Typically they have one table and serve only your group that evening.
Have a great time, Steve. Keep cool, since it is usually very hot and humid there (think New Orleans) at this time of the year.
Larry