I'm going to suggest something that I haven't seen suggest by anyone else, as it goes against the current fashion.

Try looking for/at bike models with a horizontal top tube, and avoiding frames with compact geometry (slopping top tubes). The frames with sloping top tubes with all result with you either the seat too low (improper fit because you can't extend your legs), or too long a top tube (you end up feeling like you're too stretched out), or if you go with a small frame as some people have suggested (you will feel like you're curled up in a ball).

On a bike with a conventional top tube, I think it would be easier to find a bike with the right seat tube length (for your leg length without an overly long seatpost) and the right top tube length (look at models with a shorter than average top tube length, like Women Specific Models). With a properly sized horizontal top tube frame, you shouldn't have a problem with the "stack" being too short, and the handlebars being too low.

On a bike with a horizontal top tube, you might fit a bike with a frame between 56, 58, or 60cm. Smaller frame will have a shorter top tube, so try riding bikes with a 56cm frame, and go up progressive until you are happy with the fit.