Who is best at promoting chess? Should FIDE be the one to promote chess.  Or USCF and other national NCFs?

Should it be tournament promoters who profit from more players attending?

Is it the job of local clubs to promote chess?  

All of the above??

I have seen local clubs fail because they promote chess instead of promoting the club for the benefit of the players in their town.  I see small towns have successful clubs with no dues and many rated events with dozens of players ,  when some larger cities charge too much, throw the dues money around like they printed it, and rarely have a rated tournament which is usually very poorly attended. 

Clearly tournament promoters need to promote chess so they can generate profits. 

FIDE needs to promote chess with less urgency as they are the one in charge of chess and the size is less important to them, but still significant.

National federations would tend to be in the middle although IMHO leaning more to needing the members to pay dues so they can survive and thrive.

Now I see that some schools promote chess.  WHY?
Simple answer: it is everybody's job to promote chess.

FIDE stands for "Fédération Internationale des Échecs" which stands for "International Chess Federation". It is their job to promote international chess - 

World Championships
Candidates tournaments
Continental Championships
Olympiads

It is the job of the national federations to promote chess at the national and regional level -

National Championships
National Leagues
Regional Championships
Regional Leagues

It is the job of clubs and their affiliates (in some countries the national federation is also run completely by the clubs) to promote chess at the local level

Local Leagues
Local congresses

It is the job of internet companies to promote chess online (although FIDE and the federations sometimes like to try as well)

It is the job of rich sponsors to fill in the gaps and provide the icing on the cake. Here I'm thinking of lucrative, major opens like the Isle of Man, Gibraltar and the big events run out of St Louis Chess club (and bankrolled by Rex Sinquefield) 

No one group of organizers is best overall. It would be ridiculous for FIDE to try and run every minor city league. It would be equally ridiculous for clubs to run the World Championships.

Note that I haven't mentioned entrepreneurs for the simple reason that making money from organizing chess tournaments, while possible, is extremely difficult. Whoever can crack the TV market and turn chess into a sport with the same televisual appeal as soccer deserves to be a billionaire.