When you enter a taxi, you are starting into a business transaction. You are paying, and he/she is driving. As soon as you enter, the taxi driver will be waiting to be told where you want to go. Start out by saying something like "good afternoon". Then state exactly where you are going: "I'm going to Penn Station" or give an address "I'm going to 1234 Lenox Ave.". That's all. You can also say "take" or "drive" (but not "carry" - that would be for your baggage), and it is always nice to use the magic word "please": "Please take me to 1234 Lenox Ave.". It's more of a command than a request. You're not asking him to do you a favor. I would only say "can you take me..." if I thought there was a legitimate reason why he might not be able to take you.

I chuckled when I read this. I lived in New York City for a few years and took a taxi from the airport many times. The odds are that your English is much better than the typical New York taxi driver's English, so don't worry about it too much. A simple "Grand Central Station, please" is all you need. Verbs just add confusion! Anyway, that's how I see it.

“Can you get me to New York” works and we can understand what you’re saying, but “Can you take me to New York” sounds more formal.

Take

Can you drive me to the new york