What can I enter into Part IV, line 2 AGI of New York State taxes for my spouse if they are a nonresident alien? Can I still e-file with Turbotax?

To clarify, are you manually filling out these forms? If you are filing jointly, you would include her worldwide income in the federal return and the AGI information would automatically populate in the NYS return.

Since she doesn't have a SSN or ITIN, you could not file electronically, You would need to print and mail the return in and print NRA in her social security field. Here is how to report in your federal return. 

First, prepare your return reporting all your income and your spouse's income including all worldwide income.

1. When you get to the Let’s get ready to e-file screen, select File by Mail.
2. Attach a statement to your return, signed by each of you that states that one of you is a U.S. citizen and the other is a nonresident alien and that you’re electing to both be treated as U.S. residents for tax purposes. Include the full name, address and Social Security number (or Individual Taxpayer Identification Number) of each spouse. This won’t affect the immigration status of the nonresident alien.
3. Mail the return to the address on the instruction sheet that prints with the return.

If your spouse doesn’t have a Social Security number or ITIN, you’ll need to apply for one when you mail in your return. To do this, follow steps 1–3 above and then do this:

1. Fill out Form W-7 and attach it to your return, as well as all necessary documentation. Click on the link to download a pdf copy to fill out and attach to your return.
2. Mail the return to the address specified in the Form W-7 instructions.

Note: TurboTax will give you an error regarding the missing Social Security number for your spouse. Ignore this since you are mailing your return.