We lucked out as parking was still available at 11AM on a Thursday at Navy Pier (flat rate fee $30). As you approach the "U" loop there is an overhead arch showing how many spaces are available.
We did have a backup plan for parking in case the parking garage at Navy Pier was full. Btw, you want to use the EAST garage as its closer to the ships in case walking is a problem for anyone in your party.
There are other options as well such as parking further away and riding the trolley to Navy Pier.