I'm an NRI living in US. I want to transfer about 60 Lakhs INR from my NRO account in India to my US bank account. Entire money need not be transferred in one shot. It is fine to transfer it in parts. What is the best way to transfer it with minimum fees/taxes
I want to transfer about 60 Lakhs INR from my NRO account in India to my US bank account
Yes you can. However there is some paperwork you need to follow. As per FEMA [Foreign Exchange Management Act], any transfer by individuals outside of India need the 15CA & 15CB form. The 15CB is from a CA to state that taxes have been paid on the funds being transferred. The limit is 1 million USD per year. Read more at Liberalized Remittance Scheme and here.
What is the best way to transfer it with minimum fees/taxes
Assuming you were already declaring the funds held in Banks outside of US in your regular IRS filings, there is no other formality. Question on Minimum fees service recommendation is out of scope on this site. Outward remittance can only be done by Bank Transfer.
The best way is to approach your bank and fill out a transfer form to send USD to your US account (if you are visiting India). They will require quite a number of proof (AADHAR, PAN, Passport) copies.
Otherwise speak to your bank about how to do a wire transfer from your India A/C to US; after de-moitization regulations have tightened, the best course of action would be to speak to your bank directly.