The last time I was at Solstice, they were selling bottles of beer for $2, the same price as 12 oz. cups of coffee. Although it is far from being a bar, Solstice is not merely a Cafe. Their coffee tastes fine, and refills are offered for $0.25. Also, the staff are very competent, providing efficient and friendly service.
Furthermore, the seating is comfortable, there is free wireless internet which can be accessed by using a password they provide, and the ambiance is one way or another, depending in when you go. During busy hours, such as on the weekend, in the mornings, finding a seat might be difficult. Later at night, however, the place is quiet. The lighting is on the softer side.
All of their products that I have tried were satisfying. There is one couch in the corner which I find particularly enjoyable, and the choice of music seems atmospheric. For example, they were quite prominently playing indie rock and dance genres during the times I visited. Solstice is situated on University Way, also known as The Ave, near the University of Washington, in the University District. With over a half dozen coffee shops along this half mile stretch, hopefully some of the details I have provided will help to narrow down your choices. I recommend it to anyone looking for a place to relax and enjoy a drink.