3 by 1.5 inches, at least.
Just like with Table Number Signs, you want them big enough so your guests can find their names, but at the same time, you don't want them too big to distract from all your other table decorations, like your pretty flowers and tableware.
TIP: If you have place cards, color-code them with the food option your guests chose on their RSVP card so the wait staff knows what to serve.