Your question is very broad. The best neighborhood for you depends on the lifestyle you seek - urban, rural, walkability - and your work commute and price range. To start getting a feel for Seattle and it's neighborhoods, I can provide you with some great materials.
First, go to http://www.buyandsellseattlerealestate.com and start searching. Once you are attracted to a few properties, you can click on the Market Insider Tab and get information on demographics, schools, amenities, etc.
At my website, http://www.karenmcknight.com , you can click on the button to the left called "About the Area". I have links to great information on the different neighborhoods in the Seattle area.
I can also "snail mail" you a book that has great information and insights on Seattle area towns and sites to see.
Let me know how I can help,