Further to the west is the village of Pyles (or the unfortunate alternate spelling, Piles) with lovely views to Kassos and Crete. Sample the local honey here. That's Pyles on the left.
Far north, the inland village of Olympos is a wonderful spot to visit at Easter to see the traditional dances and celebrations. Women still bake bread in outdoor ovens and dress in beautiful traditional garb. This striking village is draped over a mountain ridge topped by windmills. The views are magnificent. The houses are adorned with painted balconies, often stacked one atop the other, and somethimes opened with ancient wooden locks and keys. Stop in the church for a look at the frescoes and iconostasis.
Olympos was isolated for so long that people here still use pronunciations and expressions that can be traced back to the Doric and Phrygian dialects. Many of its men are noted musicians, but property is passed down through the mother.
From Olympos you can drive all the way north to Avlona, inhabited only in summer by farmers from Olympos who use tooks that would look right at home in a museum. From Avlona you can walk down to Vrykous where there's a tiny chapel and rock-cut burial chambers.
The first beach north of Pigadia is Ahata. It's small but very clean and with pebbles. Parts of the road are unpaved but possible with care. There is a taverna.
The second beach north of Pigadia is Kyra Panagia. This beach is rocky but has all the amenities and most of the road is paved.
From the paved road that took you to Aperi you may descend by dirt road to Apela Beach but its easier and safer to take a water taxi from Pigadia. Arrange to be picked up again, too!
Bring food and drink because you'll be on your own at Apeia Beach.
The fourth beach north of Pigadia is Agios Nicolaos. This is a sandy beach close to Arkasa and may be reached by car or motorbike. On the south side of the island the water is a couple of degrees lower then on the east side. The waves are bigger and body surfing is possible. There is a restaurant and sun beds and parasols for hire by the hour.
In Lefkos, locals recommend the Pine Tree restaurant. There are several good eateries in Pigadia and the smaller towns all have two or three good choices.