NASA wouldn't need to transmit anything to reveal our location to most the universe,
We as a planet produce hundreds of thousands of radio transmissions that don't just stop at the edge of our atmosphere, they will all escape into space and directions wouldn't need to be transmitted, it's very easy to work out what direction a radio signal is coming from and with two separate sites receiving it is even easier to triangulate the precise position of the origin.
Nasa themselves also operate a deep space radio network for transmitting to far away space craft and receive signals back from them, this too would be detectable by any other being right across the universe (given enough time) and again, no details would need to be included in the transmissions for the exact position of their origin to be worked out.