I know the city square always starts with 2 food, 1 shield, and 1 gold. I'm pretty sure you do get a river commerce bonus, when applicable. Also, I read somewhere that if you build on a BG tile, that you get the extra shield after size 6. I don't know that you can take advantage of any food resources in this way though. I have also not seen any benefit when I settle on an iron, for instance.
Edit: just checked a game save and the one city that's built on a resource (a horse), is getting one more gold, (the horse bonus) than I can otherwise account for.
HTH