(You need an apostrophe between the "n" and the "t" in "don't.")
Usually, I would say
"I don't have the address or the location."
So #1 is correct. It's clear, and it's natural.
In real life, if I wanted to be even clearer, I would say
"I need the address and the location."
This makes it clear that I expect TWO pieces of information. It also avoids all questions about the usage of "either," "neither," "or," and "nor."
#2 is wrong. The word "either" is in the wrong position.
#3 is wrong. The word "neither" is in the wrong position.
If we wanted to be very clear or slightly formal, I would say
"I don't have either the address or the location."
I could also say
"I have neither the address nor the location."
#4 is wrong. We can make it correct by adding two words:
"I don't have the address, nor do I have the location."