Here's a version as sung by Jack Teagarden. I've put in (versions of) the most salient chords (I use others and more varied too, but the essence it there).

(Mary Coughlan has also recorded this and sings "If you're feeling gloomy, come around and screw me", IIRC.)

Mick

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MEET ME WHERE THEY PLAY THE BLUES
Steve Allen & Sammy Gallop

(Cmaj7)I got a heart that's broken (C9)hearted, how can I (Gm11)mend it? (C7b5)
(F)I got a crying jag you (Dm7b5)started, how can I (Fm7)end it?(Fm6)
But (Cmaj7)if you're feeling(C#dim7)gloomy, (Dm7)come a-(Cdim7)running (Ab9)to me,
(Cmaj7)Meet me (Am7)where they (Dm7)play (Ab7#5)the (G7#5)blues.

People have said they've seen you dance in hide-away places
People have said you find romance in other embraces
But if your mood is dreamy, and you care to see me,
Meet me where they play the blues.

(C7)Eyes that (Dm7)flirt with a (A7)tear, or (Dm7)come on round (A7)here
And (Cmaj7)misery loves (Dm7b5)company, they (Cmaj7)say.
Though they (D9)linger til (Am11)dawn(D7b5) while the (D9)trumpet wails (Am11)on(D7b5)
(Dm7)Hoping you'll happen this (G7#5b9)way(G7#5).

I'm getting tired of sipping wine and watching it bubble
How did our dreams get out of line and wind up in trouble
But honey if you're learning, there's a flame still burning
Meet me where they play the blues.