It depends on the audience rather than the venue for me.
Lots of times I have a room full of older people for Texas in town for the Casinos.
They would totally ignore most of the stuff on Russ' list. Probably has to do with geographics as well.
In non-country settings, here's some off the top of my head that I do that seem to work for most everybody.
Spanish Eyes
Last Date
Summer Wind
Summertime
Margaritaville (sorry Russ)
Can't Help Falling in Love
Unchained Melody
Besame Mucho
Fly Me To the Moon
You've Got a Friend
Fire and Rain
Yesterday
If
LOVE
Mona Lisa
I Just Called To Say I Love You
Now or Never
Stand By Me
My Girl
Color My World
A Place in the Sun
Always On My Mind

Songs like these are recognizable, even if they aren't paying close attention. Many of them have been done in a variety of ways and by various people, so almost everyone can identify with them.
And then someone will request Brown-eyed Girl anyway.
DonM