I just completed a fascinating 3 weeks in Ponta Delgada at the Calheta Suite apartment (which included a visit from my brother from NY). The apartment is lovely, really well situated only a half block from the waterfront and a five minute walk to the harbor where whale and dolphin watching tours depart. It feels surprisingly roomy for a small flat -- 2 bedrooms, 2 bath rooms, a small kitchen with 2 surprises, a washing machine and a small adjoining balcony from which you can hang your clothes out to dry AND view the Atlantic!
The hosts were so friendly, and generously supplied many brochures about Ponta Delgada and Sao Miguel island, and some complementary bread and cheese and coffee. The backside apartment neighbors are also friendly, and one even raises poultry, so occasionally you can hear roosters crowing!
I recommend you visit Ponta Delgada and stay at the Calheta Suite