Once you have chosen one or more of the alternatives, you can really enjoy La Gomera. There are numerous insanely great hiking trails. The hiking trails lead past gorges and valleys, over numerous mountains and through impressive forests. La Gomera is incredibly diverse and the nature is amazing. In parts, it has a bit of an old dinosaur island (Jurassic Park, perhaps).
There are a few places that are suitable for overnight stays and are at least somewhat connected to the bus network. One is the capital San Sebastian de la Gomera, although there are hardly any circular hiking trails from here, so I can’t necessarily recommend the town as a starting point. Better located and with more hiking possibilities are the towns of Hermigua, Valle Gran Rey and Vallehermoso. Vallehermoso is also home to the only real hostel with shared rooms, called Telegraph Hostel. It’s an incredibly clean hostel with a great roof terrace and a wonderful view over the town. Valle Gran Rey is probably the most touristy place and offers many hiking tours. My two hitchhikers also stayed here and it is true that there are mainly Germans in the town. At one time, many hippies settled here, and they still try to create a good atmosphere on the beach. In Hermigua there is an unbelievably great beach, but it is very difficult to reach. It is called La Caleta and you can use the public barbecue areas here free of charge with a great view of the Teide and set up camp for the night.
Finally, a few pictures to bring the atmosphere a little closer.