Is there any American bank branch (like Citi, or Chase..)  or other bank network which is connected with major US banks in Nepal where I can put money and take out here in US

or What is the best way to bring some money from Nepal.......

thanks

Open a city bank account

I don't know how much money are you planning to bring from Nepal but there is a limit on the amount of money that you can bring. the main thing is Nepalese currency has to be converted to US dollor or Euro which can be done with the authorization of Nepal Rastriya Bank upon presenting a legitimate reason.

there is always other method like Hundi which is not a legal service.