The Bombay Club
If you're looking for a quiet place in the quarter to enjoy a drink or two and some bites, The Bombay Club is the place to go.
Patrons are allowed to come and go as they please, so you can enjoy the cocktails in the cool AC, then step outside to the lovely courtyard in the heart of the French Quarter.
The bar is also a lovely place to hang out during the day, and they offer a selection of 50+ cocktails, so you're guaranteed to find something that will tickle your fancy.
The Happy hour runs weekdays from 4-7, with the welcomed exception that it starts at 1pm on Fridays.
Enjoy $4 beers, $5 glasses of select wine, and $5 select cocktails inside or in the courtyard.