Your daughter is actually correct. It is an open secret to people living in the Lincoln Park neighborhood that parking in Lincoln Park itself is free and not permit restricted; to be specific, long stretches of Stockton and Cannon Drives. Unfortunately, since it is an open secret, pretty much everyone in the area tries to take advantage of it. It is almost impossible to find a spot unless you spend a half-hour driving up and down the streets waiting for someone to pull out.
Even if you find a spot, you have to watch for street cleaning, possible car burglary, and overstaying as pointed out by previous posts. It would be impossible to leave your car there for 10 days without running afoul with Streets & Sanitation or the police.