A couple suggestions.

First, go to your local bike store and look at what they have available. Even without buying, you can look at a lot of different models and types. Many new models have been made for years, so you'll have a better sense of what's out there in the used market. Don't waste their time, but have them help you find a frame size that will be comfortable for you. At 5'4", a lot of used bikes will be too big, so it will help if you can narrow down the models and frame sizes that work for you. Step over height and reach to the bars are going to be key measures for you.

For general around town riding, a hardtail mountain bike or hybrid would be a good choice. An older road bike designed for touring rather than racing is another good option.

It's usually better to get a simple bike from a good manufacturer than a bike from a department store with all the bells and whistles made with poor quality parts.

If you do buy a used bike that needs work, look for a local bike coop where you could get help fixing it up and learning repair skills.

Don't forget to budget for a good lock.