Try looking into West Seattle. There are nice safe areas that aren't too expensive, and there are a lot of new places being built there. A lot of younger people are choosing to live in West Seattle because its cheaper than being downtown, but still just a very short drive into the city...and West Seattle has a lot to do and everyone is nice. Try looking at apartments in the alaska junction or nearby there.
Seatac wouldn't be my first choice to live unless it was really close to work. First figure out where you'll be working/school and what your life style will be.
Please email me if you have any questions.
CityData.com. Good luck!