A stranger stayed in my NYC apartment, and I stayed at her place in Cape Town, South Africa. Hana Elson

Last November, fresh out of a relationship and trying to feel like myself again, I started daydreaming about a warm New Year's escape from New York City .

I desperately wanted to book a one-way plane ticket somewhere, but between flights and accommodations, a last-minute trip during the holidays was more than I could afford.

After hours of searching for cheaper alternatives, I had an idea: What if I swapped apartments with someone instead of paying for a pricey hotel?…