1503. At least she's not a syringer

There once was a woman named Ginger
Who, when she would drink, was a binger
And she sometimes would go
To the famed Alamo
After first getting smashed at The Menger.
That famous San Antonio Hotel (click) is right next door.

10/27/2014  I've been informed that the hotel's name is pronounced MING-grr, not MEN- juhr.  Thanks to Claire, here's my emendation:

A woman I met at The Menger

Didn't stay long, refusing to linger.

Left the bar and did go

To the famed Alamo

On her way out, she gave me the finger!