Low Power FM is legal in the US
The FCC allows you to broadcast on both the FM and AM band provided the emitted power doesn't exceed a maximum value and doesn't cause noticeable interference to a licensed station. Back in the day I used to use a small FM transmitter to broadcast music around the house and yard during parties (you'd just grab a few old boomboxes and put them in strategic locations to play the music). I still have the kit but its fallen into disuse because analog radio has largely been supplanted by digital feeds, feeds that include WiFi connected loudspeakers.
(The transmitter itself is quite high quality; its basically a single chip that has a frequency synthsizer and stereo modulator. I'd guess a real FM transmitter is just this chip plus an audio limiter and R/F power amplifier.)