Many postcards include pre-printed horizontal address lines to show you where to add the address. But not all will do this, so assume that the mid-right of the card is the best placement for the address.

The address side of the card must be divided into a right portion and a left portion, with or without a vertical rule. The left portion is the message area. The destination address, postage, and any postal service marking or endorsement must appear in the right portion. The right portion must be at least 2-1/8 inches wide (measured from the right edge of the card, top to bottom inclusive). [3] X Research source

You can also write right up the edge of those lines without having your message clutter or overpower the address.

While the post office won’t love you for making a mess of the address, most post offices will do their very best to help deliver your postcard.