Google "Airtel Store" and visit the nearest as per your hotel location.The staff at your hotel can help you for that.
Hi Rahul, thank you for your immediate help. This gave me a base to start searching..
Yes for all operators (Airtel, Vodafone, Idea etc.) the normal branch offices are not allowed/enabled to sell these SIMs to foreigners (it's more complex paperwork than what they can handle). However the regional offices, for a town like Gorakhpur at least 3-4 in the whole city hence one should be within 10 km from your place, can do. Visit closest store and they will refer you to the proper one.
<Erik> & [Sandya]