Where or what is the address the return of the W 4-V form to the Alburquerque, NM office?

[Rachel_W]

You will need to give your Form W4-V to the Payer of the income you wish to have the taxes withheld from, not the IRS.  

For example, if you are filling out Form W4-V to have taxes withheld from your Pension Income, you would send the form to the Payer of your pension.  If you want to have taxes withheld from Unemployment Compensation, you would send the form directly to the State paying the Unemployment Compensation.

I have included a link to Form W4-V, including the instructions here for your reference: https://www.irs.gov/pub/irs-pdf/fw4v.pdf.