Right at the heart of Delhi lies Connaught Place (famously called CP), one of the most famous places in Delhi. It's got enough restaurants and cafe for you to lose count, you can shop for anything from clothes to gadgets (including a lot of street vendors), and has the Central Park to just hang out at. It's open every day of the week.
Also, since it's so central to every place in the city, expect a crazy rush all the time.