Apologies if this is a repetitive question. I am moving to US on immigrant Visa. I do not have a NRE/NRO account, I have FD's which are maturing and I would like to en cash and take the money to US with me. Rupees when converted to USD will be less than $100M. What's the best route to do this. My Son is in the US and he is a USC. Preferably, I would like to take this money with me when I depart for the US next month. Many Thanks!
Please find out whether you are considered to be a tax resident of the US from the date that you received the permanent immigrant visa or from the date that you first enter the US on that visa. If the former, and you received the visa after April 30, you might be a part-year resident of India for Indian Income Tax purposes for the current tax year.
You need to convert your bank accounts including Fixed Deposits (the FDs that you mention) to NRO accounts as soon as possible. You will need to keep at least one NRO account open for a year or more to receive the final interest payments on your FDs as well as the proceeds of cashing in the FDs, not to mention any refunds of Indian Income Tax that may be due to you for last year or the current year. Once you are done with all these, follow the procedures outlined in this excellent answer by @Dheer to transfer the money to your US account. At this point, you can close the NRO account if you wish.
As PeterK's comment says, it is not a good idea to bring a large sum of cash with you unless you are really really paranoid about banking channels. Note that if you insist on bringing cash (whether it is INR or USD) or negotiable instruments (checks or bank drafts) with you when you land in the US, these will have to be declared on entry if the total exceeds US$ 10K. There is no limit to how much you can bring with you as long as you declare it.
Transfers of your own money from India to the US is not taxable income to you in the US, and income tax will already have been paid/withheld on that money in India, and so there is no income tax liability in India either on the sum transferred.