Any hotel in DEL will be able to arrange an airport transfer for you. I have personally gotten them from the Hyatt as well as the ITC Maurya.

As far as being included in the room rate, the club rooms a the Hyatt do, otherwise they are about INR 4,000 (if I remember correctly) each way. The price at the ITC Maurya was significantly more reasonable, INR 1,000 each way.

In any case, book the hotel you want then have them arrange the car. It's the last thing that you should be worrying about.