If you arrive at 11 PM you won't get to Times Square until 12:00-12:45 AM if you use public transportation which also includes LIRR trains from Jamaica Station. Subway will take the most time. Also consider weather during your stay.
Carmel (which may have promo codes) has an 6 person Van/SUV rate starting at $70+any tolls ( the tunnel may be faster during daytimes but probably not at that hour) + tip. There is also the larger 6 person SUV that starts at $90. I'd go for this option with an expected total cost of $115-125 with tip.
As for the Metro card option go with the 7 day.