Is there any English friendly music school in New Delhi that allows one off lessons for Sitar? Particularly one that would provide the Sitar for you.
Exactly what Mark Mayo said, just check Google next time or go to Delhi's main bazaar and ask in any of the music instrument shops, most of them offer sitar lessons and they all provide sitars for it.
Here is a one that was recommended by a fellow traveler when I mentioned this question over dinner:
Dhingra Musicals Rajat is giving the lessons in a room just above his shop and it is located at Main Bazaar in Paharganj, shop No. 1086 e-mail: email@example.com Cell: 9911043900 or 9818536666
One lesson is 700 Rp and if you want to take 10, it will be 3750 Rp but you can, of course, bargain.
You can buy a small sitar for 2600 Rp and a big one for around 6500 Rp.
This one looked the most 'friendly' I could find with a quick search.
However, it would seem there are plenty around, if you have a look at this list, for example.
So I suggest maybe calling a couple of them and seeing what they say, how their English is, and whether they provide a sitar - I suspect they would in most cases.