A good tip I heard was to scour the Ul'dah residential district first. The plots there are apparently not as sought after as ones in other districts due to how they're built. (pillars on the corners?) Following this advice, I saw my first ever actually open residential plot in Ul'dah a couple days ago, after a month or so of casually looking at other districts.

Buy one there, and build your house up, and from there you can move your house to a different district when a plot becomes available.