The directory where a tmux session is started in will be the directory that new windows start at. How do I change this starting directory without closing the tmux session?
The way to do this is to detach from the session (^b d with the default keybindings) and then specify a different directory when you reattach to it. When attaching to a session, use the -c flag to specify the working directory. Here's an example:
$ tmux list-sessions
tmuxwtfbbq: 3 windows (created Tue Apr 5 14:25:48 2016) [190x49]
$ tmux attach-session -t tmuxwtfbbq -c /home/chuck/new_default_directory
This setting will be persisted - after you've reset the working directory, you won't need to keep specifying it every time you reattach to the session.
For the record, I'm on tmux version 2.0 (though I don't think it matters - I couldn't find anything about adding a -c option to the attach-session command in the change logs so I assume it's been there for quite a while).