How was Hong Kong influenced by its geography?

A great question I would say.

The reason Hong Kong is Hong Kong because of its unique location. It is near to PRC yet separated. During the early periods it served as an important trade outpost for the British merchants. They signed a 99 year lease agreement with Qing Dynasty. Initially they traded tea and silk for clock, watches, musical box and other such stuff. But soon it developed into an entrepôt. An entrepôtis a trading post where merchandise can be imported and exported without paying import duties, often at a profit. This profit is possible because of trade conditions, for example, the reluctance of ships to travel the entire length of a long trading route, and selling to the entrepôt instead. The entrepôt then sells at a higher price to ships travelling the other segment of the route.

So Hong Kong's proximity to PRC brought in several roles for it, like:

Trading Partner - HK as final customer and as supplier buying from and selling to China
Middleman - organising transactions between China and third countries
Investor/Financier - providing and organising funds for China
Facilitator - point of contact, source of learning

GOODS
entrepot - HK firms buy from China, find buyers, set prices, take risk of ownership, make contracts
trans-shipment - goods pass through HK
brokerage - goods shipped directly from China to third countries -HK firms provide services

SERVICES
tourism - HK firms arrange inbound and outbound China travel since they allow people to visit without the requirement of a visa. In fact most of the tourists to China opt to come to HK first and get the visa to PRC from there.

The role of middleman for HK is the centre of the economy: 90,000 Import/Export firms employ around 600,000 people.

HK has a permanent geographical advantage and infrastructure development is well ahead of China because of the 99 years of British influence.

Hong Kong developed from a fishing port to a trading port. Before the trading with the westerners started, HK was a fishing port as it was along the coast line and it has a harbor. That's why you see a lot of fishing history in HK. When the westerners arrived in China, many of them landed in HK as it was closer (European ships traveled from Europe from China by going around Africa and India, so HK was closer than say, Shanghai). Westerners were interested in Shanghai and Beijing because of they were close to the "heart" of the emperor/capital. Hong Kong is one of the most southern cities of China, farthest away from the central government.

Because of the harbour, coastline and location (closer to Europe and far from the Chinese government), Hong Kong and Macau became colonies of the Brits and Portuguese respectively.

if not for the geography there wouldn't be any HK...