Peyia (Pegeia) village  is found at the centre of the bottom half of this map. Coral bay (below) is a five minute drive.  Polis is on the top right segment of the illustrated coast line. The drive to there is about half an hour.

1) Coral Bay beach for excellent swimming.
2) Agios Georgios has a quaint fishing harbour and a nice cliff top restaurant
3) Lara Bay (Akamas Peninsula) is further along via a dirt track. There is a beautiful beach which is important for turtles.
4) Baths of Aphrodite is on the other side of the peninsula. You reach via Latsi by driving up over the hill that Peyia sits on. As well as the baths, there are nature trails that take you through the peninsula.
5) Latsi (Lakki) has good fish restaurants.
6) Polis is the local town of the North West Coast which is worth a visit. 
7) Saint Raphael is a beautiful church reached if you drive along the bay north westwards away from Polis. Further up is Pomos & Pashyamos which have unspoilt beaches in idyllic surroundings.