BoA charges you flat rate of $ 45 for wire transfer. It's safe and reliable. You can do online as well. I have done multiple times and you can send much more that you have intended (just for informational purpose). You can send to government bank (that's what I did). You have to find bank code (or I guess its called swift code) which is unique to all bank though out the world. A quick goggle will do the trick. If your relatives account is in some branch, It's OK because the initially the fund will go to head office and than moved to branch account.
One point to remember - Don't send in local currency. You will get very low exchange rate. Send as $$$ and Nepal bank will convert accordingly based on the exchange rate of the day they deposit the money.
Hope this helps..
P.S. I am trying to bring some money too in few weeks or months, and maybe we can help each other.