This is centre intersection of the city. The corners used to be two banks, a department store and a jewellers (two of them are the same). The cream/white building here used to be Westpac. You see where it as "Bank of New South Wales'. It was built for Frank Hart, who had a ironmongery & general stuff sort of shop. (Not to be confused with W. Hart who had the hardware shop around in Charles Street. I think he was a son/brother. W. established the business, then his sons went their own ways, but that's from memory). It's lower level had an awning extending out over the street.
The big cream & red brick next door was the Launceston Hotel. It was one of the first hotels established in Launceston. (One of the first that has a name and location and licensee that I know, which I can't say for its predecessors.) When it was actually built is less known. I know it was in business in 1823. Its proprietor ran some advertisements in the newspaper & he is on the very first list of people licensed to sell spirits, wine & beer in the country of Cornwall. (https://monissa.com/hotels/1823-launceston/ if you're interested.) How soon before was it built? Who knows, but I haven't found any evidence of its existence before that.
Obviously that's not the 1823 building. It's been redeveloped at twice. This version is about 1903.