Hi,

As many users have already suggested, you have to use your American Passport.

1. All US citizens are required to travel with American Passport, regardless of the number of other citizenships you hold.
2. It is more of a LOGICAL quest: 
If you enter Nepal with Nepali passport, Fine! But when you exit what will be your proof to show that you can leave Nepal to come to the States?  Your American Passport right! Ah..Ha... now you show your American Passport, Nepal immigration will seek to see a visa, in which case you'd have none.  So, bottom line is you have to enter with American Passport.
3. Nepal has a very easy system.  Check with the Nepal Embassy Website.  You can apply for the visa and will be granted in TIA or you can apply directly with the Embassy here in the States via mail.  The amount varies depending on the number of days.  I think the cheapest is 15 days, then 30 or 45 days (i forgot, you can check this info in the website) and the most expensive is for 3 months.   The fees are payable in US dollars (Dollar Bills) at the port of entry or the embassy.  I do not know if TIA accept NRS but I have always paid with USD without any problem.  Just have the exact change ready.

Have a great trip and I hope this was helpful.  If you are still confused call the Nepalese consulate in New York, they will answer your queries without hesitation.