Run play-install.sh from any directory you want, this will automate the installation of play in any directory you want it. It is possibile to install through sbt by just setting up a sbt project with play as a dependency but you seem to loose the rails like magic for project generation and such (and I like magic).
Also play is in homebrew! Happy about that? Well, don't use it because it's broken! There is a bug in the play shell script launcher when play is invoked through symlinks. This is the ticket on their issue tracker: https://play.lighthouseapp.com/projects/82401/tickets/194-failure-on-getting-a-realpath-of-the-execution-file-play