As suggested earlier it's better if he flies into Delhi and sees Rajasthan or Agra.

From Mumbai I would suggest going down to GOA, it's an overnight train journey. DEC is peak season for travel to GOA so better to book train tickets in advance. From GOA he can take VOLVo buses to bangalore or the train.

For train and buses in India he can visit the website www.makemytrip.com

He can also consider going to the backwaters in kerala they are also an overnight journey by train from Bangalore.

If he decided to come to DELHI he can take the Rajdhani express train to BLR as they provide food in that train.

Hope this helps