Downtown parking is metered on the street and charged by the hour in the ramps, with rates rising for arena events and during ArtPrize. None of it is expensive by big-city standards and all of it is more annoying than it needs to be on a busy night.
The local habit is worth copying: park in a ramp on the periphery of the core, where the hourly rate is lower and the queue to leave after an event is shorter, and take the free shuttle in. On an arena night that saves both money and the twenty minutes everyone else spends in an exit line.
A few specifics that matter. Hotel parking downtown is usually charged separately from the room, so factor it in when comparing a central hotel against one a mile out. Street meters are enforced, and the enforcement is real rather than decorative. Residential streets behind the restaurant districts on the east side have permit restrictions in places; read the signs rather than following the car in front.
Outside downtown, parking is free and easy almost everywhere: the neighbourhood restaurant streets, Blandford, the zoo, Meijer Gardens and most of the parks. Millennium Park has charged seasonally for vehicle entry at the beach area, so check that one.
In winter, watch for posted snow emergency routes and overnight restrictions, which exist so the ploughs can work and which are enforced when they are declared.