Another option is to do the Agra trip by train - in a day ! ! !
We're flying into Delhi and out of Mumbai with 3 weeks in Goa in between.
There is the Shatabdi (superfast) service from New Delhi to Agra - departs 06:15 and takes 2 hours.
Returns from Agra at 20:30 back into Delhi at 22:30. Cost is approx Rs400 each way in AC Chair Car or Rs700 each way in 1st AC (private cabin for up to 4 people)
I have also managed to book these in the UK in advance - they sell out quickly and will more than likely be waitlisted by the time you arrive in India.
Another tip re: fllights - book them before you go -
http://www.makemytrip.com is good so is
http://www.yatra.com or even go to the Expedia
INDIA website for flights - for some reason the UK version does not show all the possible flights and prices avaialble.
http://www.expdia.co.in
Shout if you need any more info.
Cheers
Alfi