I've been to Ponta Delgado twice, and both times I've stayed at Praia Dos Moinhos. This is a small village located on the north coast of the island. There's not a lot in the village, there's a fish restaurant, and a bar overlooking the beach.
The fish restaurant is great, it's the kind of place where they bring out a tray of fish, freshly caught, and you choose what you want, then they go and cook it for you. The bar claims to serve the finest burgers on the island. They're pretty good. They also serve local craft beer too, so more plus points!
We stayed in an apartment overlooking the beach, with it's own private footpath cutting through the bamboo leading on to the beach. As the village is so small the bar closes around 8pm, and you're left on your own in the darkness, sat on your balcony overlooking the beach, with the sounds of the waves lapping on the beach. On a clear night the stars are phenomenal, probably the best stars I've ever seen, a place for watching shooting stars and seeing satellites go by...
There's a walk that starts in the village that takes you around the peninsula and the local countryside. It's really quite fantastic, taking in beautiful coastline and spectacular clifftop views, over farmland, both with cattle, and agricultural fields.
A highlight of the walk was around halfway around, where you take a detour down down the cliffs to the small beach, which has the remains of a Roman thermal bath. I didn't try the water (it was full of algae), but apparently it is around 30 degrees.
After a very strenuous walk back up, with the aid of a bamboo pole, the walk meanders up and down the hill sides over the open countryside before returning to the village of Moinhos, through a park area that features a beautiful waterfall and gardens. There's a water fountain there as well to fill up your bottle, which provides naturally carbonated spring water, a first for me...
After this it's a short stroll back to the bar on the beach for a well deserved glass of beer or to...moi