Which is my "home address". I am filing now for state returns.. I pay both rent in one city and also taxes on my home in another city of the same state.

Your home address is the address you use to receive mail currently, which can be a PO Box.  If you are having the fees withheld from any refund, then you do need to provide a physical address.  But the tax return itself may be a PO Box if you don't have a physical address to use.

As I recall, the program does not ask for "Home" address. It asks for "mailing" address. The address you enter here should be where you would want the IRS to mail any correspondence concerning this tax return, should the need arise for them to do so. The mailing address has nothing to do with what your resident state may be either. It's simply an indication of where you would want the IRS to send any correspondence to you, if it was necessary. (Such as your refund check if you elect to have them mail you a check.)