If I moved to NYC on June 21, 2023 from Texas and my wife moved on August 1, 2023 to NYC. Do I take an average of the combined numbers?

TX doesn't have income tax, you need to file NY part-year resident return. 

TurboTax handles part-year returns, but you need to make sure you've set up your personal information correctly.

1. Sign in to TurboTax and select My Info.
2. A Your personal info screen appears.
3. Question number 2 asks you the state(s) you lived in during 2023. Select your state of residence from a dropdown menu.
4. You'll also be asked if you lived in another state in 2023. Answer Yes and a new section will appear asking for your previous state of residence. Select the other state you lived in.
5. Fill out the date of when you moved to your current state.

Please follow the instructions in the link to allocate your income correctly:

How to enter New York State income as a part-year resident in TurboTax 

See also:

If I moved from Texas to NY in August, but my husband moved at the end of June can we both file as TX residents because I was there over 6 months? (intuit.com)