It's always tough when you have a secret you're keeping from someone close. To try to broach the subject with my wife in the early days (before we got married) I used all kinds of ploys, without straight out telling her.
I would try her shoes on as "a joke", as we're similar size foot. I would comment on heels I saw while we were out shopping, and many other little hints. None of them got the message through and in the end it was just up to me to spell it out, I like heels, I'd like to wear them.
She still isn't completely comfortable with it, although she has given me two pairs of shoes with lowish heels which she bought and doesn't like (women and their changing minds a?) and has taken pics for me of me in my heels.
As for public heeling, she is against it except for one pair of the heels she gave me which are the ones in the linked image below. Not high but not normal mens height so it's a compromise.
The advice I would give is be honest with your wife or girlfriend, don't push too hard to get what you want, each time I try to force things along it goes backwards, but if I plant a seed and let it grow in her mind and we get further forward towards what I want to do. Take it slow make small changes towards your heel wearing goals and allow your S/O time to adjust before going the next small step.