Congratulations on the new boat! The San Juan Islands are a spectacular cruising area - you could spend months here and not see it all... so, don't worry about FOMO (Fear Of Missing Out) - you will come back!
When we first bought our C-Dory, we spent a couple summers cruising the San Juans, the Gulf Islands, Desolation Sound, and all around Puget Sound. Never the same experience twice. For the past 5 years, I have been driving commercial whale watch boats based out of Friday Harbor and Roche Harbor - I am running in the areas discussed.
Friday Harbor is the "commercial hub" of the San Juans, but is still a small, quaint town. Good provisioning for groceries and a nice variety of restaurants. Weekends will be busy (even in September), weekdays will be blissfully quiet. The marina is a city-owned entity and run very efficiently. Roche Harbor is privately owned, and most folks seem to think it is more "upscale." Roche is a resort, Friday is a town... both are great marina stops.
A short travel from Roche Harbor to Stuart Island is so worth it - great hiking on the island, including a 4 mile walk to the light house, and a mid-stop at the one room schoolhouse... and the "treasure chest" (a MUST on Stuart). Two protected anchorages on the island, depending on wind direction: Reid Harbor is on the south and very protected from all but an east wind. Prevost Harbor is on the north and protected from all but a north wind. Both harbors have mooring balls and a dock (if your timing is good) - but anchoring out is great in both. Prevost does have a grassy bottom in some areas, so you may find the holding easier/better in Reid. If you use your phone/data in this area, you will likely have a good signal... from Vancouver Island; watch for international roaming.
If you like to anchor out, there are some great places in the San Juans: go into Garrison Bay (south of Roche), anchor in calm water and dinghy to English Camp, where you will learn about The Pig War, and see how the San Juans came to be part of the United States. The west side of San Juan Island puts you in Haro Strait - I am in these waters almost daily - it can be flat calm or 5' confused seas, depending on wind/current. Check weather. For the record, the whales do not hang out on the west side of San Juan Island - my job would be much easier if they did. If your timing is fortunate, you could see whales anywhere in the San Juans - there are federal and state regulations regarding distance to the whales and speeds you can operate in the vicinity of whales. Just know that closer than 200 yards and you will likely get cited/fined. Some people think you can drive up ahead of the whales and shut down, essentially "allowing them to come to you"... this is a HUGE NO-NO, and you will get blue lighted. Don't do it. They are amazing to watch - do it from a respectful distance. These are some of the most protected mammals in North America, and NOAA takes it seriously.
If you go south (also called "down island" on the west side of SJI) and come through Cattle Pass, know that wind against current will make Cattle Pass a "washing machine." It is another area that I go through several times each week, and it is usually pleasant - when it is ugly, I have turned a 55' boat around rather than pass through there. It is an area where upwelling occurs as the Strait of Juan de Fuca pushes in and rises up across Salmon Bank and gets constricted through Cattle Pass. The tidal currents and eddies can be strong in the pass. You may see Stellar Sea Lions and bald eagles in this area.
Other interesting anchorages: Fisherman's Bay at Lopez Island - you can also get a slip at the Islander. Blind Bay at Shaw Island - one of our favorites. There is a well-marked rock (disappears at high tide) at the entrance to the bay; clear than and you can go quite far back in the bay and feel like you are completely away from civilization. A dinghy ride to the small store at the Shaw Ferry Landing will result in ice cream.
Orcas Island has Deer Harbor and Rosario Resort - two great places to get a slip. Rosario is a full-on resort, and staying in the marina there gets you privileges at the resort. You can also anchor by Deer Harbor, but it is exposed to southerly winds.
Prevailing winds in the San Juans are south through southwest... when the wind blows from the north, things will generally warm up, but you may experience rough water. When the wind blows from the southwest, it will generally be cooler... and you may experience rough water. The two straits that border the San Juans, Rosario and Haro, can be calm or rough, depending on conditions. Again, wind against current will result in rough water and an uncomfortable ride... wait for a change in the tide, and your ride will be lovely. Most of the cruising in the San Juans is protected water, but keep an eye on your charts for rocks (they are well marked).
Of course, Sucia Island is the place most think of when you say "San Juan Islands." It is a busy anchorage, with mooring balls and a small dock. A close stop from Anacortes or Bellingham. Some people go to Sucia, then Friday Harbor or Roche Harbor, and think they have "done the San Juans"... SO much more than that.
The San Juans are a VERY special place!
If you have the time (and your passports) a trip to Victoria is a real treat - considered "the most British city outside England", it has a very international feel to it. Try for a slip in the Victoria Inner Harbour - you will have beautiful views day and night of the Parliament Building and the Empress Hotel. Buskers and artists all along the waterfront. Easy walking in the heart of the city. We love Victoria, and it is best experience while staying on your own boat.
Well, that should keep you busy for a month or so. 😉 When you have more time, I'm sure you'll get more recommendations. Congratulations again on your new boat - a very exciting time, and you will be in a spectacular area to give it a thorough shake down!
Jim