The really cool thing for you about our "Gare Central" is that unlike "Penn Station" where you are leaving from in NY, There are no sleeping homeless people to trip over every two feet.
Queen Elizabeth Hotel is right above the station. No need to go outside. Just follow the signs. You are a 10-12 minute walk from the train station to anywhere downtown. Plus that walk can be achieved all underground if you find it too cold. The world famous Crescent St. is about 12min walk West, Old Montreal is 12min South East, main shopping centres (Eaton Centre, The Bay, St Catherine St.) is about 3-4 min walk North, St. Laurent St (The Main) is a little further maybe 20min walk East. Our Cathederal (Marie-Rein-Du-Monde) is on the next block West from the station if you exit the station from the North/West side before entering Place Ville Marie. Exiting S/W you can walk 3 min west and reach the Centre Bell where the Montreal Canadians occupy last place in the NHL Eastern Conference.
Someone mentioned Vargas Steak house which is in the same building as the station but on street level, N/E corner. This excellent restaurant can be reached without exiting the building. Take a cab to the trendy fancy resaurants on St. Laurent above Sheerbrooke St. If you are in a good hotel, ask the consierge to book a reservation for you, this usually results in even better service at a restaurant.
You won't have any trouble btw to locate any of our fine strip clubs. They are pretty much North South East or West. Have fun.