24 yr old grad student looking to move to Seattle

I will be attending Bastry University in Kenmore but really want to live in or near the city. I am looking for a great social and young neighborhood that wouldn't be unrealistically far from school. There is a school shuttle from Bastyrs clinic in Wallingford that takes students to school for free.

Any advice on somewhere that might be a good fit? I've really never spent any time in Seattle.