There's a very old shop in Sita Ram Bazar by name 'Sikandar Omelette wala', people there are mad for that shop's omelette, and there are around 30 (or maybe more than that) varieties of omelette with variations. If you can visit, then do visit, I would suggest you to go in the evening by 7pm. You can ask anyone about it there, they will guide to the shop.
Rahul eggs in keshav puram
As I am vegan so don't eat omelet all, but many of my friends have told me about the Rahul egg, it is quite popular among them
You can try Rahul eggs as my frirnds go there and I have heard them say again n again that the shop has amazing omelettes
Try Rajiv Ande Wala in Palam, it serves the best omlette.