I use Constant Contact (which is a pay service, not free), and I am able to customize my footer with the address I choose, NOT the address I sign up with. So I am able to be a city and state, but not a specific address. I've been sending emails out for years that just say "Proudly South Austin, Texas" for my address. Maybe I'm in violation, but it's been fine for at least eight years. Pay services may have more leeway since the email is tied to a credit card and not just a sign-up email.
It's $16 a month for up to 500 email addresses. I keep my list lean by having everyone reopt in every six months. I get upset when I'm reported as spam, as they were the ones who signed up! Anyway--this is Constant Contact: http://tinyurl.com/appa77v