Go with the plan for a longer 9 night stay. As you already understand, the weather there is unpredictable all year long. I once had very rainy, windy, and cold weather for two weeks straight in the month of August. Go figure!
With nine nights, you can split your lodgings definitely between two locations, and even pick a third. I always encourage travelers to the Azores to think about their evenings and the ability to enjoy nighttime walks, with the availability of restaurants. Furnas lake sounds nice, but is quite isolated and not a great long term location. This is not a good base for any stay on the island if you plan on exploring.
The island is very big, and there are literally thousands of interesting spots to visit. Driving times will be longer than you think. For me, and thinking of your time frame and how and where you will explore, I would choose 3 nights in Ponta Delgada, 2-3 nights in Furnas village or Povoacao, and the rest in the Ribeira Grande area.
If you have not read the post at the top of this Portugal forum titled "Azores Islands Travel Advice", I encourage you to do so. There is a link embedded in the post (written by the webmaster) directing you to my Azores Travel Guidebook. The first 52 pages are absolutely free to read. Probably any question you can think of for visiting these truly enchanting islands will be answered in those pages. Then you can peruse all the driving and walking day trips I designed for Sao Miguel and all the other eight islands.
If you choose to purchase my digital book, you will have all the detailed information for Sao Miguel. Now you can fine-tune your days and nights as well as your accommodation locations according to where you will visit.
I am always available for questions through private message.