On-street parallel parking is allowed on most streets in downtown.  The posted time limits apply M-F until 6:00pm, unless stated otherwise.
Parking near Main & Washington as well as Main & Nelson tends to fill up first.    So if you see space on other nearby streets, grab it.
There are also several public parking lots.  ONLY 3 of them do not have time limits as noted on the map below.  
There are no fees for parking on street or in the lots.
All three of the long term parking lots are south of Randolph Street near the Visitors Center.
INSIDER TIP:    Go for the County Court House parking garage (#1) below, 20 S. Randolph Street, between Nelson and Washington Streets.  Much easier than driving around and parallel parking.   It’s FREE & no time limit.  It fronts on Randolph Street to give you easy access to shops/restaurants.  And its lowest level is easy access to Washington Street, across from the visitor center.W&L downtown parking lot (2 of 4)

Here’s another map that is clickable, scroll in to see street names.

Legend for map?  Click the icon in top left corner of map. Directions? Tap the parking lot name on the legend or on the map & tap the directions icon on the upper right.