Suyog sir, you definately need a visa to enter Nepal. According to Nepali Constitution 2047, any Nepali is allowed to hold dual citizenship so, I assume you have given up ur citizenship when you take US citizenship. So, as an American Citizen, you need tp pay the full visa fee which is not free at any Nepali Embassy. The price of visa fee depends upon the Nepali embassy you r dealing with. As far as i Know, its £95 at Nepali embassy here in UK.