The answer is yes! I walked to all three of those places from the Bayview Hotel. They will give you a map/directions at the front desk.
The walk to Giant’s Causeway was beautiful and uncrowded. One starts off from the Town’s car park, walk a bit along a beach around a small bay, and then start off on a path on the headlands. The views of small secluded coves were amazing. Along the way is a small memorial to a military plane that crashed there during WWIi. You enter the Giant’s Causeway area through a small gate. On the way back we chose a different path that follows the old tram track down the hill.
The other two sites were completely walkable. For Dunluce Castle we stopped there on a walk to Port Rush and then took a bus back from Port Rush.
It is easy to combine walking with public transport.