It is not too far to walk – go up over the hill past the Hotel Port Lligat, past the campsite and down the hill into town. It’s about 15 minutes to get there and a scenic heart raiser.
You can walk to the lighthouse either by the road (about 1 hour) or by a coastal path (about 2 hours) that is signposted off the road about 1km from the house. The views from the Cap are spectacular and there is a bar at the lighthouse and a restaurant in the old Fort building above where you can get a meal or just a cold beer whilst sitting out taking in the views.
A fantastic area to visit on the way to the lighthouse is Tudela, where you can see spectacular rock formations, many made famous by Dali. You can, of course, also drive and there is parking both at Tudela and at the lighthouse.
Starting in Cadaqués you can walk all the way around the coastline, coming across some lovely little bays and bars along the way. Follow the bay around to the left in Cadaqués as you are looking out to sea, past Plaja Ses Oliveres, where there are two good chiringuitos (pop-up restaurants) and across to Plaja Ros (where there is another nice bar, S’Olivar des Ros). On the far side of Plaja Ros you will see some steps where the coastal path starts that winds all the way around the coastline.