A nice hike, the Point Elizabeth Trail, connects Rapahoe, just north of Greymouth, to a northerly "suburb" of Greymouth, on the north side of the river. This is probably most practical if you can be dropped off at one end and picked up at the other end.
Visit the biggest and less crowded glacier - the Fox Glacier located 2.5 hours drive south of Greymouth.
Take a day trip to Christchurch or to Arthur's pass. catch the train to Arthur's Pass 1.30 departure and coach back to Greymouth 5.15 at arthur's Passarrive back to Greymouth at 7pm