Thank you all. I was looking at my options so that I can choose a specific flight and time from Delhi but  it looks like it might be better to do all flights in one itinerary .

Do they ask for documentation such as I-20 or Green card only when returning back to the US or also when flying to Nepal? If you are on your way to Nepal, can you just hand the passport and nothing else? I don't see a point of handing them anything else and risk the chances of losing them.