Not a lot if time to see this beautiful island but if it was me I would drive to Playa de Santiago and sit under the tree in the square with the locals and watch the world go bye before going to the rustic cafe on the beach for the best basic seafood you have ever tasted.
After lunch drive around to Valle Gran Rey and stop at the viewing point to take in the magnificent views over the valley before driving down to the beach. Walk along the promenade to Vueltas port and watch the world go bye.
Take the time to appreciate what la Gomera is all about. In particular the Garajonay National Park, the smaller, non touristy towns, and the high villages. Start early. Take the North road out of SS to Hermigua then the road on to Agulo where they are doing a great job of restoring the old buildings in this very small town. Onwards towards Vallermosa but look for the road if to the left to the visitors centre. (Luis restaurant at the road junction, excellent for a traditional gomeran lunch - try sopa de berros). The visitors centre well worth visiting if you have time. Back on the road towards Vallermoso. You'll have some great views. From Vallehermoso onward towards VGR but it's a long drive down and back up to Gomera's main tourist town. Turn off to take the road across the to of the island and through the forest, looking out for the turning to the villages of Chipude and El Cercado. Stop in El C to visit the traditional potteries and the lovely small pottery museum there. The road from here back to SS takes you beck across the top of the island, stop at the various viewing places, particularly Los Roques to see the huge rocky cores of the ancient volcanos. Finally back to SS. Enjoy. Come back again. Stay longer.