What "futuristic" songs play during Bioshock Infinite and when?

Question

Minor spoilers warning

We learn during the game that Albert Fink, Jeremiah's brother, was able to listen to music through Tears and claim it as his own. During the game, you can hear "oldified" version of songs that came out after the game's timeline.

I've heard Cyndi Lauper's "Girls Just Wanna Have Fun" through a tear (but not its old version) and during the end credits I've heard a version of "Everybody Wants to Rule the World" by Tears For Fears (Ha!).

What is the full list of all the futuristic (as of 1912) songs that appear during the game and when do they appear?

Answer 1

Song	Location
God Only Knows by The Beach Boys	Welcome Center
Girls Just Wanna Have Fun by Robert Hazard (another version was recorded and popularized by Cyndi Lauper)	Battleship Bay
Tainted Love by Ed Cobb (originally recorded by Gloria Jones)	The Graveyard Shift (the bar in Shantytown)
Fortunate Son by Creedence Clearwater Revival	Bull Yard
Shiny Happy People by R.E.M.	Port Prosperity
Everybody Wants To Rule The World by Tears for Fears	Memorial Gardens

^{Sources:
BioShock Infinite end credits
BioShock Infinite IGN Wiki, "Secret Song Covers" article
@hammar's comment on this answer}