From Positano you can easily go to go to the isle of Capri, the city of Sorrento, Amalfi and the village of Ravello that is one of my favourite towns for its views,
The ancient Church of Positano, its Roman villa just below the church, the ruins of Pompei and Ercolano that are one hour by taxi and one hour and half by pubblic transport, the ruins of Paestum that are one hour and half by taxi.
The path of the Gods is one of the most beautiful and scenic places of the Amalfi coast. There are also other beautiful hikes around the area and I can give you tips regarding it as I am a hiking guide but first of all a nature lover.
Close at hand you will find many beaches, restaurants, good food and good wine. I also do pizza classes, so if you could be interested please have a look on my website positanopizzaexperience.com