Tropea is by far the biggest attraction nearby. The beach is amazing as is the church (walk up on the roof and visit the garden behind the church). It costs a couple of Euro. Walk up the stairs to the old town if you do not want to park up there. There is a large and good parking near the center. Do not miss the view of the beach at the bottom of Corso Vittorio Emanuele, near Gelati Tonino.
Faro Capo Vaticano, about a mile south of Tropea. The best view in the region!
Scilla, about 80 kilometras to the south, both Chinalea, the castle and the beach. Beware of blue line parking lots if you do not buy a parking ticket!
Sicily is amazing, for example Taormina. Very nice but very popular! A visit is a whole day. The ferry between Villa San Giovanni and Messina costs just over 30 Euro for a car no matter how many passengers. Bluferries are a bit cheaper than Caronte.
Bova (superiore), about 150 kilometres to the south. Calabria’s best view!
Reggio Calabria if you want to see a larger city. Lungomare, museums etc.
Pizzo, Centro Storico with many restaurants and cafes. Ice cream at Bar Ercole. Ice cream factory Callipo at the lower entrance to Pizzo (Marinella).
Boat trip from Tropea! Both Stromboli (Stromboli by Night) and the great excursion, all day to Vulcano, Lipari and Stromboli.
Wine tasting in Lamezia at Statti vineyard. An interesting tour followed by tasting a selection of their production of white and red wines with suitable snacks in nice facilities.
The caves at Zungri are just over 10 km from Zambrone and can be an interesting excursion for just a couple of hours.