If your Form 1099-R was mailed to you at an Arizona address, that should be entered into TurboTax. If it was sent to your current address in Texas, use that address.
When adding the information from a Form 1099-R (or any of the 1099 series forms) to your tax return, your name and address should automatically populate based on the personal information you entered into TurboTax when you began your tax return.
However, if this information does not match the information printed on the Form 1099-R by the Payer, you should edit the pre-populated information to match what is on the form. This includes the Zip code. It will have no effect on the taxability of your earnings, but will assist the IRS in matching your income to the forms submitted by the Payer.