My daily commute takes me over the Montlake cut. I have ridden around the city a fair amount and I think heading south over the Montlake cut is one of the most convoluted sections of road for bicycles in the city. The Seattle bike map will have you cross to the east side of 25th Ave on a pedestrian crosswalk and "bike salmon" down the sidewalk on the wrong side of the street to cross the bridge. This is usually how I do it. If you remain on the right (and correct) side of the road, you can stay in the lane on the really rough metal grate if you have wide tires. But don't even think of it if its wet. I did once, hitting the grates with a decent amount of speed and fishtailed the entire way over the bridge, thinking the whole time I was going down and the car behind me was going to run me over. So you ride onto the pedestrian sidewalk, and once you have crossed the bridge you get to hop the curb back onto the road and try to merge into the lane with cars that are impatiently trying to merge right back across you for the ramps onto 520. Then if you want to get to the arboretum you have to quickly and dangerously merge all the way left to a turn lane to cross the traffic in the opposite direction. The traffic light here doesn't detect bicycles, naturally, so if no car is with you in the lane you get to wait until a car joins you or try to cross against the traffic light with a steady stream of high speed traffic from the 520 off ramp. If I was new to the area I would have no idea how to navigate it by bike. Riding north across the montlake interchange isn't so bad but it still forces you to either ride on the extremely rough grate or ride on the sidewalk with pedestrians. Most ride on the sidewalk.
The Fremont and University bridge crossings are completely straightforward in comparison.
I sure hope they get the 520 rebuild right. I am happy that the new mayor is trying to get the new bridge fitted for light rail. The current plan will take out a nice chunk of the arboretum and have nice westbound high speed exit ramps but the eastbound ramps will still be only one lane. And it won't be suitable for light rail. I'm thinking that will be nice for eastside SOV commuters and that's about it. Its a short sighted and small minded plan.