The Registrar’s office has posted future facility hour schedules on their website, which can be found here. On the bottom of the webpage, each excel sheet will have information on which buildings are open and the hours.
In addition, they have posted information about study options, and the link for reservation of a seat for final exams is now live:
https://go.illinois.edu/examseat.
The Illini Union have study space set aside in both Room 103 (aka Colonial Room) and the 2nd Floor Ballroom. The Lower Level Food Court is also open for studying (with limited seating ) and is generally quiet with the vendors being shut down.