From there...you are fine
I'd imagine it would be a straight shot down madison into the loop...even if there *were* bad neighborhoods in the middle, you are on a bike so it would not be a problem
I am about the same distance but to the south and I often ride king drive and it has never been any trouble compared to riding the lakefront. You don't see many bikers but the whole thing has a bike lane and the side streets are empty around there and red lights are super visible in both directions so you can intelligently skip red lights. That ride will take you through far worse stuff than you will see on the way out to oak park