The amazing thing with Hong Kong's central district is not that it houses THE financial centre of Asia but that it still coexists with a collection of long-standing businesses in old shophouses, much of which is the heart of Hong Kong's cuisine.
You can start the day at Sang Kee for a breakfast of congee and fried vermicelli. This congee institution has been around for much of Hong Kong's modern history and is famous for its fish congee and pig's giblets congee. The fish in particular is extremely fresh and despite it being a river fish, has no foul muddy taste. Accompaniments of a ginger/spring onion soya sauce is excellent with the fish. Do also order the fried vermicelli, well fried to envelope each strand with a tasty stock and with hardly a grease trace. Dace fish cakes are also good and springy.
After Sang Kee, take a walk to Lan Fong Yuen for a taste of one of Hong Kong's oldest and quintessential Cha Chan Teng. Sip on smooth silk stocking milk tea (the cold one is excellent with even ice cubes made from the tea so there is no dilution), while biting into a thick toast smothered with peanut butter and condensed milk, the stuff our childhoods were made of.. And if you have room, or are just greedy, try their famous chicken chop with tossed Nissin noodles, served with a ginger/spring onion condiment for a little bit of tasty innovation.