By default, Homebrew gets installed under /usr/local. This is great, because it doesn't require you to use sudo to install and upgrade packages. But the downside is that it turns your /usr/local directory into a git repository. If you don't have any conflict with this, then by all means, stick with the default.
I had a conflict. Specifically, I use nave for node version management. Unfortunately, both Homebrew and nave drop a README.md in /usr/local, which means nave frequently modifies a file that's under Homebrew's version control and brew update breaks.
Solution
I decided to "move" my Homebrew directory to ~/Homebrew. Here are the steps I followed:
I didn't document this as I did it. Hopefully, I didn't forget anything.