We stayed in Capital Hill and strongly recommend it - residential yet lively with restaurants, shops and bars within walking distance, and close to a subway station. Fremont is a neighborhood we also liked a lot with its own culture and nice parks, though a car might be necessary. If planning on going to certain restaurants, try making a reservation as they get popular and our friends who live here all made reservations for most outings. Seattle has a very cool modern public library very worth a visit/recharge. Starbucks Reserve roastery is also fun.