Dive bar drink prices?

We spent five and a half days in New Orleans last week, starting New Year's Eve. We were impressed by the grace and acceptance the city shows in living through what needs to be lived through.

I have a minor question. On NYE, I went to a dive bar next to the hotel to have a drink. I started to order an old-fashioned, but switched to a Sazerac. The bartender said 'You realize you're ordering a Sazerac in a dive bar?' I agreed. We had a nice chat about bourbons, after he served me a Sazerac in a plastic cup. The tab for the drink was $16. I tipped liberally, and restrained myself from asking whether this was a tourist price.

Later in the week I ordered an Old-fashioned at Commander's Palace. The tab was $16. It is possible that this is the standard price for a cocktail in New Orleans. But it reinforced my notion that $16 at the dive bar was the tourist price. Any comments from locals?