This site has a ton of good travel information from places to stay, things to eat, etc.
A 1st century BC villa that was discovered in 2000 which is now a museum, including frescos and ancient artifacts.
There is a famous hike called Path of the Gods that a lot of the travel sites end up recommending if you’re in the Positano area, the hike takes approximately 3 hours. We’ve attached a nicely detailed link about the hike.
There are tons of shopping options in Positano, you can easily spend the day wandering around town looking at shops and art galleries. Positano is famous for its handmade leather sandals (which they make right in front of you) and their lightweight linen clothing (I have a white dress that I got there in 2017 which still gets compliments).
Positano has quite a few pebble beaches to enjoy, please note that you’ll likely have to pay a small fee to use the beach/rent chairs.
Quite a few blogs have recommended this nightclub which is built inside of the cliffs of Positano.
The Mitchells went here in 2017 and we recommend the guided tour through the site since you get the most information about the city that way. It should be noted that the majority of the artifacts found here are actually now at the Naples National Archaeological Museum.
Another archaeological site, it’s smaller than Pompeii but is better preserved and more complete than Pompeii. A lot of reviews online said people preferred this one.
Lots of water sport options! You can charter boats for fishing or just enjoying the water, go kayaking through grottos, go snorkeling, or swimming. TripAdvisor has a lot of resources and reviews for the different activities and companies.