The length of the top tube is the most important measure, followed by the height of the head tube.

I'm your size and ride 60cm bikes, with 59 to 60cm top tubes. I like to sit up a bit higher, so I go for ~20cm head tubes. I also have gorilla-long arms, which may explain my preference for a long reach.

If the frame is too big, you'll be stretched out too long, which is hard on your back, shoulders and hands. Also (from personal experience) you'll have to work hard to avoid knee issues (from your weight being far forward), crappy power up steep hills (from your center of gravity being too far back over the rear wheel) or saddle sore problems (hips being canted too far forward so you put weight on your taint instead of your sit bones). You can compensate a bit with a short stem, but then the handling of the bike suffers. Try to keep around a 90-110mm stem for your size.