All mints have relatively low salt tolerance. Is there a location that is somewhat protected from ocean spray? If you water the plants frequently, and perhaps hose off the leaves after a particularly strong off-shore wind, you will dilute the salt effect. It's worth a try.
Many plants can be negatively affected by salt spray, and plants that are native to seaside areas have adapted to the salt spray. But mints are usually tough, so your peppermint could very well do fine. It also depends on how high above the ground and how far from the ocean your balcony is. The only way to know is to try it!