With that much time and a desire to "do the sound", I'd suggest a trip that essentially circles the Kitsap penninsula. There are two Port of Allyn launches that only about 4 miles apart - one is in the Hood canal and one in the sound. You could pretty easily start at one and end at the other. I haven't used either of them so perhaps others can comment on the quality of the launches.
This
link should bring up a map with them on it. They are #'s 39 and 40 on the map. The trip on the east side of the penninsula is more urban so there are fewer (but still plenty) of places to anchor out/hike but there are better restaurants and city things to see. I'm not super familiar with the south end of the sound but have poke around a couple of places.
On the south end of Vashon Island, Dockton park is has some nice floats and is a cheap stay - I think you could easily anchor out in the harbor there and it's very well protected and fairly quiet.
One night in Tacoma might be nice as it would give you an opportunity to see the glass museum - lots of handblown glass, very beautiful. Blake island state park is a C-brat and SeaDNA favorite. Good floats and some nice walking. Also, some native american entertainment and food in the summertime - that aspect is a bit touristy but you don't have to partake and the rest of the island is nice.
I'd recommend a stop at the Bell Harbor Marina for restocking and for hitting some nice restaurants. You can walk up to the Pike Street Market and buy that sockeye salmon you want (plus lots of other great food). The water front in that area is fun to visit.
Eagle Harbor on Bainbridge is very protected and easy to anchor in. There is also a city float that allows O/N moorage for a few boats and free tie-ups for less than 2 or 3 hours. The local village (Winslow) is a nice walk with some interesting artsy-fartsy shops. At the north end, Port Madison offers some good protect anchorage but there's no place to really go ashore except for Fay Bainbridge state park on the NE east side.
You could chose to go through the locks and cruise down past Lake Union and into Lake Washington - good views of the city, some good restaurants and many nice parks are available. Plus, if you're close friends with Bill Gates, you can stop by his house on Lake Washington. :lol:
The Port of Kingston is a good place to refuel, buy food etc. It's very quick in and out. By the way, plan on buying your fuel on the Penninsula rather than the East side if possible. Fuel is generally less expensive on that side as you aren't paying the higher Pierce or King county taxes.
The Port of Edmonds has a good bait shop (Bud - the often grumpy bait seller), good restaurants and transient moorage. Very nice marina.
You could chose to also circumnavigate Whidbey island. Coronet bay at the north end is quite nice. Good anchorage and good hikes on the island. Deception pass is worth the trip - it's best to pass through there on a slack tide as the currents in the channel can get upwards of 10-12kts. I've done it up current at max flood and it can be safely done then too.
On the way up, the Swinnomish channel and a stop at La Conner might be nice. There's a good marina there and a nice sleepy town to visit. The Port of Everett also offers good transient moorage.
The hood canal leg would be much quieter with more opportunity for hiking etc. I'll put together some recommendations for that later.