I'm looking at exactly the same trip later this year and am thinking about a trip to the Taj Mahal. This will need two nights as Europe flights arrive in the morning and the Singapore connection leaves around midnight.

My plan would be to go to the Holiday Inn near the airport and see if I could check in a couple of hours early, if not have lunch and lounge by the pool. The Taj tour will pick you up at 2.00am for a 2 1/2 hour drive where you get to see the sunrise plus some other sights. Back to the hotel around 6.00pm to clean up have dinner and head out to the airport.

If you are only doing a 12 hour layover I would book the hotel for a day and take a shopping tour of Delhi. There are a few reviews on Trip Advisor to help you choose, be careful of which airport hotel as there are a few dodgy ones.