Found it

Once I used the flash on my camera, I was able to find the port.

It is not located in the lamp.
It is not located in the big phone.
It is not located in the small phone.

It is, of course, located on the leg of the table.

I'm humiliated to report that I needed to call the front desk (twice) at midnight. Both times, the operator had no clue where it might be. When someone finally came up, and we found it (together, because she didn't know either), I asked why they hadn't made a sign. And she said, and I'm not making this up: "Because it's in a different spot in every room."

Thanks to all who hazarded a guess.