Monday 9pm, there should be lots of places that are relatively deserted. As someone who regularly travels and eats late in visited cities, it's always been my observation Monday nights are the slowest restaurant night there is, everywhere. None of my options are tapas-focused, but they have apps.
L'Orignal is in a relatively obscure quiet corner of Old City. The food is good, and I've been there a few times on a Monday night at 9 or 10pm, where it's very low-key. Haven't been since the fall though. I've definitely seen client-SP -looking dates here, so I guess others think it's discreet, too (?).
The Vieux Port Steakhouse is typically fairly empty, especially once you go in off-peak-hours. And the second floor is generally out of the line-of-sight of passer-by's. Dark interior, relatively low ceilings, conversations are muffled and don't carry through the dining room. Food is not great, but decent. Sorta like hiding out in the open, with its location.
Le Bourlingueur has a back room that is hidden from sight. The restaurant is almost always empty for dinner service. More lunch than dinner is my impression. Small cozy restaurant. Food is simple, but well done. Bad bread, but the apps are good, and it's relatively cheaply priced for Old Port. Ceilings are high, though, so if you're loud...
