Where do I enter the information for a form that states "takes the place of federal forms 1099-G and 1099-INT"?

Form 1099-G would be for money received from the government, like unemployment compensation. There is a section for unemployment in the "Income and Expenses" section in TurboTax.

Form 1099-INT would be for interest income. It is entered in the "Interest and Dividends" income section in TurboTax.

So, you need to enter the income in TurboTax based on what type of income is being reported.