How close to town do you want to be? Or are you looking at something more rural?
Seattle has gotten pretty big, I was born and raised there and I now live in a small town about 100 miles north. I think a lot of people who haven't been there think of Seattle as being much smaller than it really is. It's a long and narrow metropolitan area from North Seattle to South Seattle and has over half a million people. You are not likely to find a "cabin" in the city limits. But there are dozens of small bedroom communities that might work for you. Issaquah is one, especially around Pine Lake. What do you consider "modest"? Depending on where you want to live will be what determines the cost of a small cabin on an acre of land. You won't find that within the city limits... land is at a premium. IF you can find anything in the city that is more than 1/2 acre plan on paying between $300,000 and $500,000.
What you are looking for is often called a mini-farm and those are mostly in outlying areas like Bainbridge Island and Vashion Island, which means you will have to commute by ferry. If you go outside of King County, you could try Auburn, Puyallup, Enumclaw, Maple Valley, and up north of Everett. Count on about an hour commute each way if you have to work in Seattle.
A lot of depends on where you will be working. I hope you will not consider a move until you have visited the city and area at least once and already have a job waiting for you there. The job market and housing market at the moment is not very good.
If you are not already a member of City Data, I suggest some research on the Seattle page of that site, it's set up for people moving to a new town, and you can get opinions from both locals and people who have already done what you would like to do.
If you live anywhere outside the downtown core of town, you will need a car, although there is a big push for public transportation because traffic is awful!!!
You also don't say where you live now, but Seattle's weather is another thing to consider. While we don't get nearly as much rain as legends say, there is considerable amount of gray cloudy days, and if you aren't use to that, it can get rather depressing. Which is one of the reasons why coffee is big here.
Oh, just should also add that the cost for a Washington state drivers license just went up and it now costs about $80 to get your first one. I don't know about any place else, but people here were pretty upset about that. Driver's license renewals went from $25 to $45.
I'm not trying to discourage you from moving here, I love this area which is why I've lived here all my life (62 years), but just want to caution your to get as much information as you, visit before you move and not think that Seattle is Utopia. It has it pluses and minuses just like any other place.