There is a free underground parking garage that is a short to medium walk from the archives. I have only had a problem parking there when something special is going on such as the governors State of the State speech or the inauguration of new legislators. You access it by exiting Rt. 29 at Memorial Drive and following the signs to the Capitol Complex. You can also enter from State Street. You need to show ID when entering the parking garage.
When using the elevator to exit the parking garage press the PL (Plaza) button. This will take you to ground level. Upon exiting turn left, go to State Street, and turn left again. You cannot use the Plaza exit to enter the garage. You can enter the State Library and take an elevator which requires you to change to a second elevator. Very confusing. I walk to the State Street entrance and walk down the ramp to the elevator.
Curt