I believe there is metered and/or free parking at the 31st Street Beach. I believe you can only access it from the northbound lane of LSD, so you may have to exit and swing around.

Parking here, you have your choice of riding north or south and getting good mileage in. If you've ever ridden to Museum of Science and Industry, you've seen these lots that abutt the riding path but probably didn't make note of it.

I agree that the paths between Belmont Harbor and Navy Pier are awful. The only time to do serious riding is early morning any day of the week. I'm planning on two loops of Bike the Drive - starting promptly at 5.30 before the families take to the roads...!