Filming Buildings, Schools, government buildings, skyscrapers without permits or permission?

I am shooting a feature film in the next month, and there is a certain university's library which I wish to include in the background. I don't want to get permits due to it being no budget, so I will be filming the actors walking along a similar path, and with visual fx with track the famous library in the background as if they were there.

Do I need any permission for this?

I will be doing this in front of two schools, one in Los Angeles, and one in Mexico, but both are famous.

Since were on the topic, can anyone with expertise on the matter give any extra info such as, is one able to shoot any building, public, private, government owned, and include it in a feature film without permits, permissions, if visual fx or shooting off their property is the method of including the historic building in the shot?

I.e, Eiffel Tower, Dodger Stadium, White House, Private Corporation owned Skyscraper, etc.

Thanks!

Clint Nitkiewicz Hernandez
www.newelementproductions.com
Film-Maker/ Blu-ray Author/ Compositor