Welcome to the Seattle area. We kept our boat at Shilshole Marina for about a year and then at Harbor Island Marina, under the West Seattle bridges, for 13 more years.
Blake Island is always fun. There are a number of park buoys around the east, north and west sides. Some wakes from ferries. Anchoring can be tough as the bottom drops off steeply at least on the west side. Nice hiking throughout the island and there is a small harbor on the NW tip.
Poulsbo and Port Orchard/Bremerton are good destinations. Poulsbo has a large public guest marina and anchoring is good in Liberty Bay. It is shallow, but we've always been able to stay afloat. Great town with lots to eat and shops to visit. Port Orchard and Bremerton have guest moorage at the two marinas. Anchoring not recommended in that area. We usually stay at Port Orchard and use the foot ferry to Bremerton. We have heard that Bremerton marina can be tough to navigate due to currents and the wind can whistle through there too.
Edmonds Marina - easy walk to town. Lots to do and eat. Nature preserve near the marina. Small guest dock, best to call ahead. No anchorage.
Port of Kingston Marina - Guest moorage, WA State Ferry terminal, good eats and the cheapest diesel fuel we have found in the Seattle area. Again, call ahead in peak season for moorage. Limited anchoring space.
Manzanita Bay, Bainbridge Island - On the way to Poulsbo, over on the west side of the island. Anchorage only. Quiet. No easy shore access.
Port Ludlow - Guest moorage at the marina and a large anchoring space. Not many places to eat near the marina.
Blakely Harbor, at the southwest tip of Bainbridge Island. Medium deep anchorage until you get way inside. It's a popular spot, with views of the Seattle skyline. Beware the floating patches of green stuff. A little wave action gets in if it is windy.
Des Moines Marina. Very nice town. Call ahead for moorage when the salmon are running as the guest dock fills with fishing boats.
Gig Harbor - just a little further from Seattle than Dockton, but totally different. Narrow, short and shallow entrance, but not hard to navigate. A great destination with plenty to do and eat. Guest moorage can be tough to find, but anchoring is good in the large harbor. There is a public dock with power that is usually busy. First come first serve. The famous Tides Tavern is on the south side.
I jumped around a little but guide books for Puget Sound are plentiful. We have visited these places many times. Over the years, some places have changed a lot, usually for the better, and some just look the same, which is also nice.