Coal has been a major mining activity on the West Coast and Greymouth was historically a service town for the mines. There is still some mining left, but tourism is increasingly important, including the TranzAlpine Express tourist train which comes in each day from Christchurch.
The main feature of the town is its centre and the walkway along the Grey River, all the way to the famously dangerous river mouth. Cool on a nice day but the place rather lives up to the name when the weather is not so clear! At least there are good cafes to compensate. There are typically rugged West Coast beaches to the north and south of the river mouth as well.
If you want to take a side trip back in time, then drive inland to Blackball. This is a dot of a place made famous by its relationship to the New Zealand Labour Party, a local salami sausage business, and a couple of other interesting pieces of local history.