Delhi is a rather mysterious city, partly because it completely surrounds the small (and more famous) district of New Delhi. This is a huge metropolis that most people find shocking upon arrival, with conspicuous displays of poverty and decay through most of the city.
Compared to the rest of India, except for Mumbai, Delhi is relatively expensive as well. It’s really best to stay for a few days at the most and spend more time in smaller and more interesting cities. Hotels and hostels in Delhi are not particularly cheap, except for perhaps in the backpacker ghetto of Paharganj.
Good news is that most of the city’s attractions are free or cheap, and that you can (and probably should) hire a private car with a driver for a very affordable sum.
Food can be quite cheap if you are happy to try the stuff sold at street stalls all over town, but air-con tourist restaurants will definitely eat into your budget. Alcohol is tough to get in most of the city, though people at your hotel can always arrange to deliver it for a small fee.