The pace of the Azores is slow, and slowly is how you should discover them. There are 9 islands in the archipelago and if you were to attempt to see them all, you would need a few months to do them justice. Should you try to visit too many islands in a short period, you will end up spending a disproportionate amount of time waiting in airports or queuing at the car rental desks.
If you only have a few days, São Miguel is the best Azores island for you. It has the most direct flights, there's plenty to do, and you won't waste time traveling between islands.
If you have a full week to explore the archipelago, you could opt to spend four days on São Miguel and three days on one other island. From São Miguel in the summer you can go by ferry to several islands. You could choose Pico for volcano-climbing and wine-drinking, Faial for whale-watching, Flores for hiking and mountain biking, or Santa Maria for beach-hopping.
Geographically, certain islands naturally pair themselves together, which you should keep in mind to optimize your trip. São Miguel and little Santa Maria are close neighbours. There are daily flights between the two islands and you’re only in the air for about ten minutes or 3 hours by ferry boat. A short hop that opens up a whole new island for you to explore.
If you are planning to skip São Miguel, many travellers when landing in Ponta Delgada, catch a short SATA flight to Faial or Pico. Both islands are well-connected to Lisbon by air – Faial more so than Pico; there are daily flights in and out of the former and bi-weekly flights for the latter. Flights to Faial from São Miguel take less than 1 hour.
The classic pairing for a two island stay is Faial and Pico. You could easily spend 3 days in Faial and visit Pico in between as the ferry only takes 30 minutes. They’re also very well-connected to each other: a regular ferry service sails back and forth between the harbour towns of Horta and Madalena all day long. Both islands have their own unique draw – Pico’s famous for its rugged volcanic landscape, the mountain of course (Portugal’s highest peak at 2351m), and it’s vineyards. Faial is home to one of the Azores’ most spectacular sights: the vulcão dos Capelinhos, site of the last major volcanic eruption on the island.
Heading west brings you to the island of Terceira. Internal flights with SATA international from São Miguel is the easiest option, flying time is approximately 40 minutes. Terceira is a big favourite of mine: it has a fascinating history, great food and some really cool architecture. Like São Miguel, Terceira has a smaller neighbour: Graciosa that you could easily add to your trip.
If you have more than 1 week, I would definitely recommend Flores and Corvo (the most remote corners of western Europe). Flores is a beautiful island with a great profusion of flowers (hence the name) breath-taking waterfalls and beautiful volcanic lakes. You will also find a few black sand beaches, cliffs rich in vegetation, welcoming locals but very few tourists. If you are looking for peace and tranquility, you should definitely consider it. As touristic facilities are limited on both Flores and Corvo, you will need to discover them slowly and should therefore skip them if you are tight on time.