This topic came up when one parent wanted to fund $1000 per month into their college kid's account.
What is an allowance? An allowance is an amount of money given on a regular basis. It may have rules or stipulations on under what circumstances it is received (for young children it may be for doing certain chores) or "just because we can" with no rules in place for how it must be spent.
Let's start with, Your college kid should not have time to fiddle around (even if it's in NYC) to spend that kind of cash every month. Unless they are getting an Underwater Basketweaving degree, they should be studying. Being a theater arts major shouldn't require attending expensive shows every month either.
If and how much to give your teen will depend on your circumstances. If all of your teen's bills are paid for, then an allowance might cover a tank of gas each month, car expenses such as oil changes and registration, and one decent meal at a restaurant.