If you Google for this you'll find a lot of wrong answers. tmux
rename-window is useless and will break if you do like sleep 1 and
switch windows. Fortunately tmux has an escape sequence you can use too.
First you have to enable it in tmux.conf:
set -g allow-rename on
Then to get the current working directory put this in your shell prompt:
echo -en "\ek$cwd\e\\"
And to show vim's current file you can put this in vimrc:
set title
set titlestring=%t
if !empty( $TMUX )
set t_ts=^[k
set t_fs=^[\
endif
^[ is an actual ESC (0x1B) character, which you can type in vim by
doing ctrl+v then escape.