Two alternatives:

1. I just tried out using Google Maps, using the "bicycle" option, and it recommended the way I would take. Basically Fairhaven to Eastlake, across the University Bridge, then up to your address. Google maps is estimating that trip at about 26 minutes, which I say is fair.

There is a fair amount of traffic on Eastlake, so be careful there. You can take some side streets if you'd like to have a bit less traffic.

2. Google Maps shows an alternative as well -- instead of going up the east side of Lake Union, you can take the bike route through the parking lots that parallel Westlake Avenue up to the Fremont Bridge. Cross the Fremont Bridge, then get on the Burke Gilman trail and take it to the U-district. This is a bit longer, with less traffic. Some people don't like riding this route because the route through the Westlake Avenue parking lots can be a bit perilous (cars parking, not watching for bikes, etc.).

I know that where I work, bike commuters coming from the U-district debate these 2 options all the time.

#1 is a bit shorter; #2 is a bit longer. I think #2 would seem flatter as well.