First, different restaurant, bars, etc. will take different approaches. In some countries, ones that are small enough are allowed to play broadcast media, like a broadcast radio station, without any license as long as they don't charge for it. But this doesn't apply to streaming, like from Pandora.
The most expensive approach is for these to negotiate with all the PROs for blanket licenses from each one, which allows basically any song to be played, but that's also the most expensive choice so usually only done when there's a lot of live bands playing. These restaurants could play your song, and it wouldn't have to be on any particular playlist, but they wouldn't need to play it from Pandora.
A lot of bars and restaurants and stores negotiate with big music libraries, which I consider a type of sync, and which is cheaper. But in that case, the music libraries usually make the playlists. To get on these, you'd have to search for and submit your songs to various music libraries, and long and short you usually end up making a noticeable amount less than a comparable number of plays not from a music library, but you would hope to more than make up for that in volume. But in this case, the music libraries have tens of thousands of songs and make their own playlists to meet client needs, so your song might not play at all. And almost never would a specific bar or restaurant give input on specific songs, rather the overall mood of the playlist they want, things like that.
Pandora has a service I think called cloud cover or something like that where if a restaurant obtains a specific type of membership, they can effectively be serviced by Pandora like how a music library would typically service a restaurant. It's sort of the same as the above, Pandora's editors who make the playlists can choose from basically all the songs on Pandora and restaurants and bars aren't giving feedback on specific songs.
So, generally, if your song is super-popular and one of the top songs on Pandora, and it fits the mood or theme of a particular editorial playlist, then it has a much better chance of getting on a editorial playlist, including these that might be played by restaurants with this type of membership.
As an additional pro tip, one thing that wasn't obvious to me at first, and this comment is applying to Spotify and not necessarily Pandora, but I would expect it to be similar on Pandora, is that to get on any of the really big and important editorial playlists, one first needs to be considered (by Spotify any way) in the top 50%-60% of their most popular artists. And by popular, I mean artists with lots of high quality, recent streams. You can google "Spotify Popularity Index" to understand more. And to have an artist popularity index that high, one needs to have multiple really popular songs.
