Any suggestions for a week's accommodations for 4 adults and 2 young ones?
For a first visit, I suggest staying in Ponta Delgada. There are dozens of great hotel options that are available on booking.com. Use the search filters according to your needs and budget. I suggest getting one with a pool, and most come with free breakfast. Don’t worry about parking, as there are many free lots throughout the city.
If the rooms do not show that they can accommodate more than you require for beds, email the hotel and ask. Then book directly with them.
If you want everyone to stay together in one rental unit, try searching VRBO, Airbnb, or a similar website.