There are many common question such as 'How to create a new window in the current directory'. Here are some simple how-to, inspired by tmux FAQ.
1. Preparing - set environment variable by PS1 in shell
PS1='$([ -n "$TMUX" ] && tmux setenv TMUXPWD_$(tmux display -p "#I") $PWD)${debian_chroot:+($debian_chroot)}\u@\h:\w\$ '
How it works?
$([ -n "$TMUX" ] && tmux setenv TMUXPWD_$(tmux display -p "#I") $PWD)
The previous half part makes the magic, #I indicates the index of each displays. In display 1, it saves current directory ($PWD) into environment variable $TMUXPWD_1, corresponding to $TMUXPWD_2, $TMUXPWD_3 ...etc.Just type 'printenv |grep TMUXPWD' and you will know everything.
${debian_chroot:+($debian_chroot)}\u@\h:\w\$
Well, this is my own prompt (such as walkingice@my_laptop$ ), you can keep your own settings by 'cat ~/.bashrc |grep PS1'2. Create new window in current directory
bind-key c run-shell 'tmux neww "cd $(tmux display -p "\$TMUXPWD_#I"); exec bash"'3. Split window in current directory
bind-key h run-shell 'tmux splitw -v "cd $(tmux display -p "\$TMUXPWD_#I"); exec bash"'Caution: I prefer Ctrl-a h to split horizontal window(splitw -v). In other words, when I click Ctrl-a h, I am saying "Hey, give me a horizontal line". I think it make more sense than tmux original key binding.
bind-key v run-shell 'tmux splitw -h "cd $(tmux display -p "\$TMUXPWD_#I"); exec bash"'