How Can I Replace Our Leaking Outdoor Faucet?
Your indication of where it leaks from suggests that simply repacking the valve stem might fix your leak, without having to change the faucet.
If you do change the faucet, if the pipe in the basement is threaded, just unscrew it - either the pipe in the wall will unscrew, or the faucet will, and if the pipe in the wall is what unscrews, you can remove it from the faucet after it's out of the wall, attach it to the new faucet, and thread it back into the wall.
If your pipes in the basement, including this one, are soldered, you may need to unsolder it inside and pull the valve &amp; pipe out to change the valve. One way or another that would require gaining access to the pipe.