For first timers considering Christmas in India, the beguiling combination of the capital, Delhi; Agra for the Taj Mahal and the highlights of regal Rajasthan would be perfect. The blend of seductive cities such as Jaipur and Udaipur, the beauty of rural Rajasthan and the chance to see tigers in Ranthambhore National Park is hard to beat, but it's important to note that Northern India is not going to be boiling hot at this time of year. That said, we're talking a very civilised mid teens, which might not be such a bad thing for an itinerary that includes several cities and game parks.
If heat is the key consideration, then India still works, but visitors will want to head to the south of the country, with the best beaches in the charming southern states of Kerala and Karnataka. Kerala in particular has a fascinating colonial history (you could even celebrate Christmas in Cochin in one of the many churches), elegant yoga retreats and beautiful backwaters work well as a standalone destination, or as a twin centre trip with the north.
One final thought - you'd be amazed how many months ahead of Christmas and New Year the best hotels and flights get booked up, so we would strongly recommend planning WELL in advance.