How can I get zsh to show the current path in the prompt?

Oh my, omz is setting the PROMPT variable. Let's get you a temporary bash-like prompt in your current zsh session.

PROMPT='%m:%1~ %n%#'

Your omz installation is hosed. I recommend that you uninstall it. Install it again, if you want to or read the following sections of the zsh manuals.

man -P 'less -p "EXPANSION OF PROMPT"' zshall

to craft your own custom prompt in your .zshrc and if you are interested in themes

man -P 'less -p "PROMPT THEMES"' zshall    

Although OP is already using the 'Agnoster' theme, if you are not using a theme which shows the "working directory" as desired, then it may not show the path. You need to go into .zshrc and change the ZSH_THEME="agnoster".