If you absolutely want as close as possible, there is an on-site transit hotel run by the Plaza Premium people who operate the lounges (it's downstairs at the car park level). I haven't stayed, and it's quite difficult to determine the quality from the reviews on Tripadvisor, as they seem to be a mixture of reviews of the hotel and reviews of the lounges:

http://www.tripadvisor.co.uk/Hotel_R...a_Pradesh.html

The airport Novotel does have a useful shuttle service, too, and is 3.5km from the terminal.

The Vivanta is at Begumpet - the site of the old airport. That's a fair journey from the new one - make sure you're looking for Rajiv Ghandi airport!

Personally, I don't bother staying at the airport for early flights. I tend to work in Hitech City, and so stay there, and the journey in the early morning isn't terrible (can be done in 30 minutes in a standard Meru or Skycab). And I'm very fond of my new preferred hotel up there (the Trident). But that's a matter of personal choice.