Naturally, the top one is Billy Joel’s “Piano Man.” No song will ever set the tone of a bar better.
I also love Tom Paxton’s Saturday Night.
What other songs are set in a bar?
All I Wanna Do - Sheryl Crow
We are drinking beer at noon on Tuesday
In the bar that faces the giant car wash
And the good people of the world
Are washing their cars on their lunch breaks
Hosing and scrubbing as best they can
In skirts and suits
Good lord - how much time do you have?
Three quick ones - Misery and Gin, Bartender Blues and More to be Pitied than Scolded. “Too much beer and wine. Too many good times. The lure of the honky tonk wrecked her young life.” 
Two off the top of my head are “Gimme Three Steps” by Lynyrd Skynyrd and “Lola” by the Kinks.
“Coward of the County” by Kenny Rogers
“Escape (The Pina Colada Song)” by Rupert Holmes
“Single Bars and Single Women” by Dolly Parton, written by Michael O’Donoghue
“Third Rate Romance” by Amazing Rhythm Aces
“Queen of the Silver Dollar” by a bunch of acts, written by Shel Silverstein
Okay, I messed up the title. I was thinking of songs set ENTIRELY in bars.
“Tubthumping” by Chumbawumba
Joe Diffie’s “Prop Me Up Beside the Jukebox (If I Die)”
Well, scrap songs 1, 2 and 4 in post # 5 then…
“Saturday Night at the Twist and Shout” by Mary Chapin Carpenter. I know the exact bar well. It was in Bethesda, MD and I once had to step over a very drunk Root Boy Slim to get to the men’s room there.
“Copacabana” by Paul Allen
So far as I can tell, the patrons in Semisonic’s “Closing Time” haven’t yet left the bar by the song’s end They’re on their way out, but lingering from the bartender’s perspective.
Bruce Springsteen’s “Glory Days” is arguable. The part about him staying in the bar to catch up with the ol’ baseball player is in the first stanza. But is that a frame story in which The Boss is recounting the rest of the song to the ballplayer at the same bar? Or are the stanzas about four separate independent encounters? In the latter case, three of the four stanzas either take place in a bar (Stz 1 & 4) or describe being at a bar (Stz 3). Stanza 2 – about the girl “that could turn all the boys’ heads” – takes place in the girl’s home with Bruce and her having drinks.
“Before The Kiss, A Redcap” by Blue Oyster Cult
So grab your rose and ring side seat,
We’re back home at Conry’s bar
The blond girl with her tattoo,
Reds and wine, cokes of course…
“One Bourbon, One Scotch, One Beer” by John Lee Hooker unequivocally takes place in a bar.
George Thorogood’s incorporated “One Bourbon” as the second half of a cover medley with another Hooker tune “House Rent Boogie”. “House Rent” opens with the line “Want to tell you a story …” If the singer is either addressing the bartender or another bar patron, then the entire medley takes place in a bar.
Frank Sinatra’s “One More for the Road”
*It’s quarter to three
There’s no one in the place except you and me
So set 'em up, Joe
I got a little story you oughta know
We’re drinking, my friend,
To the end of a brief episode
So give me one for my baby
And one more for the road …*
Kenny Rogers’ “You Picked a Fine Time to Leave Me, Lucille”
Tom Waits-The Piano Has Been Drinking
Heck, most of Tom Waits stuff is in bars.
Trees of Mystery in ‘Mooks On Parade’ is an incredibly obscure, fucking amazing album that is set up as a single set list performance in a bar. The first track is the MC thanking the previous act and introducing the band and the last track is the band finishing and the bar shutting down, so technically every song is set in a bar, even tho every individual song isn’t about being set in a bar. That link goes to a playlist of the entire album.
Moonshine Bandits are a ludicrously silly and catchy country/rock/rap group and perhaps unsurprisingly, several of their songs take place entirely in a bar. Check out Super Goggles and Dive Bar Beauty Queen.
And, of course, Hunters & Collectors brilliant Carry Me is set entirely in a bar.
“Hey Bartender” (the version I’m familiar with is by The Blues Brothers)
No mention of George Jones’ “Bartender’s Blues” or Merle Haggard’s “Swinging Doors”?
Amazing.
“The Bride Stripped Bare by ‘Bachelors’” by the Bonzo Dog Band is about a doing a gig in a pub.
Much of “Dixie Chicken” by Little Feat takes place in a bar (in the Commodore Hotel in Memphis).