Where do I enter state taxes withheld?

There are over a dozen kinds of 1099's; we do not know what kind you have so we cannot tell you what box(es) to enter from your 1099.   What do you have?   1099R?  1099G?  1099B?  SSA1099?   etc etc etc.

You can enter the state taxes withheld with your 1099 entry.  Turbotax will transfer the amounts as payments to your state tax return.