Most definitely rent a car, and if there are only 2-4 of you then get the smallest car available. I normally look on Kayak and rent from the airport, code is PDL, from the cheapest agency. Insurance, especially the Super CDW is costly, but you will have no worries. If you stay in Ponta Delgada, you must pay to park but there are garages that do not cost much. You will find very few tourists in the Azores during this time, and no traffic, except the occasional herd of cows moving from one pasture to another on the roads. This just adds character! There are no big must see sites to visit here, as you will do that in mainland Portugal on your tour, but this paradise is very much off the beaten path and truly unique.
I was just in Sao Miguel in late October-early November, mainly for genealogy research...I stayed there 2 weeks. Our first week we rented www.vrbo.com/322100 Look it up...my comment and many others are on the website, and the owner has 2 condos available for large groups. You are in the heart of Ponta Delgada...the condo is big and stunning!!!!! Our second week we stayed at Quinta de Santana, near Ribeira Grande...go through www.booking.com to see it...this is another great option for a small or large group, but you are a 15 minute car ride from Ponta Delgada, but we loved it! We rented our own car both weeks so transportation was easy. For my other visits to Sao Miguel we stayed in different hotels, and they vary immensely...I like booking.com to see the differences. It all depends on your tastes and style of travel. The rates for the time you will be there will be very good, and there will be lots of availability for hotels so you could wait until a few weeks before to reserve for a real good deal. But if renting through VRBO, you may want to reserve early if there is one you really like.
Our home island, Santa Maria, is a short 15 minute flight away from Sao Miguel if you really want laid back relaxation and simply BE with nature, with absolutely no tourists for a few days. Our family swims at the Praia Formosa (beach) sometimes up until December. There is one main village, Vila do Porto, on Santa Maria. Put it this way, there is one stop light on the island (in front of the fire station), if this is an atmosphere you might want to try. I mentioned to someone else on this forum that I put together a scavenger hunt for Santa Maria which I can email if you send me a Private Message with your email address. The hunt takes an entire day to accomplish, you traverse the entire island, and we did it for our family reunion back in 2010 for one of our activities! One of the locations is a chapel built by Christopher Columbus and his crew on his return trip from America.
I hope this is a good start...but now you should look more in-depth at the websites I recommended and look over at Youtube for some videos of these islands to help lead you in the direction of the trip you envision. Based upon your interests and wants, I can come up with nice options and smooth logistics for the Azores portion of your trip to culminate an amazing Rick Steves' Portugal adventure.
So if the Azores does fit as an option of what you are looking for after Porto, we will make it work. Take care and happy planning!!!