Lots of good info here - the one thing I would add is that you should probably forget about using your commute in NYC as a way to gain/maintain fitness. The quality of riding in the city is not great even on the best (e.g. West Side) paths. You’ll be trudging along at 10-15 mph trying to avoid the Citi bikes and tourists. Coming in from NJ, LI or CT is possible but will take a LOT more time than you may think.
My recommendation would be to minimize your commute altogether and if possible live on the Upper West Side. You can get across the GWB into NJ in 15-20 minutes where the quality of your rides will be infinitely better. You will also have quick access to the 6 mile Central Park loop as well, which is good for short, hard rides if you go early enough.
I think you can go a bit faster than 15 mph, but this would definitely be an issue at night. The morning commute is pretty empty.
Also would like to note that if looking at the burbs to make sure you have other methods of transportation nearby as it will rain/snow/ice